| Preface |
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xvii | |
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1 | (28) |
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1 | (2) |
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3 | (14) |
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Gaseous and liquid states |
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3 | (1) |
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The liquid-gas phase transition |
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4 | (1) |
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Spatial correlations in the liquid state |
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5 | (3) |
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8 | (2) |
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Broken symmetry and rigidity |
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10 | (2) |
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Dislocations - topological defects |
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12 | (1) |
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Universality of the water example |
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13 | (2) |
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Fluctuations and spatial dimension |
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15 | (1) |
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16 | (1) |
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17 | (12) |
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17 | (1) |
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18 | (2) |
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Molecular hydrogen - the Heitler-London approach |
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20 | (2) |
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22 | (2) |
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Exchange interaction and magnetism |
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24 | (1) |
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The hydrogen molecule, molecular orbitals, and bands in metals |
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25 | (3) |
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28 | (1) |
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28 | (1) |
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29 | (79) |
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Elementary scattering theory - Bragg's law |
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29 | (4) |
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Photons, neutrons, or electrons |
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33 | (1) |
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The density operator and its correlation functions |
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34 | (4) |
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38 | (5) |
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40 | (3) |
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43 | (6) |
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Unit cells and the direct lattice |
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43 | (2) |
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45 | (1) |
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46 | (1) |
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47 | (2) |
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Symmetry and crystal structure |
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49 | (9) |
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Two-dimensional Bravais lattices |
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50 | (3) |
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Three-dimensional Bravais lattices |
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53 | (3) |
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56 | (1) |
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57 | (1) |
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58 | (13) |
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Isotropic, nematic and cholesteric phases |
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58 | (3) |
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61 | (4) |
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65 | (3) |
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68 | (1) |
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Lyotropic liquid crystals and microemulsions |
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68 | (3) |
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One-and two-dimensional order in three-dimensional materials |
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71 | (6) |
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Incommensurate structures |
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77 | (5) |
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82 | (3) |
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85 | (5) |
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Random isotropic fractals |
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90 | (18) |
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Appendix 2A Fourier transforms |
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97 | (1) |
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97 | (2) |
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99 | (1) |
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100 | (1) |
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101 | (1) |
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102 | (1) |
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103 | (5) |
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Thermodynamics and statistical mechanics |
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108 | (36) |
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Thermodynamics of homogeneous fluids |
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108 | (9) |
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The first law of thermodynamics |
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109 | (2) |
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The second law of thermodynamics |
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111 | (1) |
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The third law of thermodynamics |
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111 | (1) |
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112 | (1) |
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113 | (2) |
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115 | (1) |
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116 | (1) |
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Statistical mechanics: phase space and ensembles |
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117 | (5) |
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122 | (1) |
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Spatial correlations in classical systems |
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123 | (4) |
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127 | (5) |
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Symmetry, order parameters, and models |
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132 | (12) |
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135 | (2) |
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137 | (2) |
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139 | (1) |
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Appendix 3A Functional derivatives |
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140 | (2) |
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142 | (1) |
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142 | (1) |
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142 | (2) |
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144 | (69) |
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146 | (5) |
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151 | (1) |
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The Ising and n-vector models |
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152 | (7) |
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The nonlocal susceptibility and the correlation length |
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154 | (2) |
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156 | (1) |
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Some mean-field transitions |
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157 | (2) |
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The liquid-gas transition |
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159 | (9) |
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The critical point and the critical isochore |
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162 | (3) |
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165 | (3) |
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The first-order nematic-to-isotropic transition |
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168 | (4) |
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172 | (16) |
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173 | (2) |
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175 | (4) |
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He3 - He4 mixtures and the Blume-Emery-Griffiths model |
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179 | (2) |
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Bicritical and tetracritical points |
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181 | (3) |
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184 | (4) |
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The liquid-solid transition |
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188 | (10) |
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189 | (3) |
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192 | (1) |
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Improvements of the theory |
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192 | (2) |
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194 | (1) |
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Density functional theory |
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195 | (3) |
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Variational mean-field theory |
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198 | (15) |
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198 | (2) |
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The mean-field approximation |
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200 | (1) |
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201 | (1) |
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The On classical Heisenberg model |
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202 | (2) |
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204 | (4) |
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208 | (1) |
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209 | (1) |
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209 | (4) |
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Field theories, critical phenomena, and the renormalization group |
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213 | (75) |
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Breakdown of mean-field theory |
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214 | (3) |
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Mean-field transitions revisited |
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216 | (1) |
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Construction of a field theory |
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217 | (9) |
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217 | (2) |
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Lattice field theories and their continuum limit |
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219 | (2) |
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221 | (2) |
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Mean-field theory from functional integrals |
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223 | (2) |
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Breakdown of mean-field theory revisited |
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225 | (1) |
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The self-consistent field approximation |
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226 | (4) |
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The n-vector model in the limit n → ∞ |
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229 | (1) |
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Critical exponents, universality, and scaling |
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230 | (7) |
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Exponents and scaling relations |
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230 | (4) |
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234 | (1) |
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235 | (1) |
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236 | (1) |
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Theoretical calculations of critical exponents and amplitude ratios |
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237 | (1) |
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The Kadanoff construction |
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237 | (5) |
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The one-dimensional Ising model |
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242 | (6) |
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242 | (3) |
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Decimation and renormalization |
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245 | (3) |
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The Migdal-Kadanoff procedure |
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248 | (8) |
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The Ising model on a hypercubic lattice |
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248 | (4) |
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General properties of recursion relations |
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252 | (1) |
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The Potts lattice gas and krypton on graphite |
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253 | (3) |
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Momentum shell renormalization group |
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256 | (32) |
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Thinning of degrees of freedom and rescaling |
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256 | (4) |
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260 | (1) |
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261 | (2) |
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263 | (4) |
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n-vector model with cubic anisotropy |
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267 | (2) |
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269 | (1) |
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270 | (3) |
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Dangerous irrelevant variables |
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273 | (2) |
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The utility of the &epsis;-expansion |
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275 | (1) |
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Appendix 5A The Hubbard-Stratonovich transformation |
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276 | (1) |
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Appendix 5B Diagrammatic perturbation theory |
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277 | (6) |
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283 | (1) |
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283 | (1) |
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283 | (5) |
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288 | (65) |
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289 | (9) |
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289 | (1) |
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Boundary conditions and external fields |
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290 | (2) |
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The Josephson scaling relation |
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292 | (1) |
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293 | (2) |
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Long-range order, quasi-long-range order, and disorder |
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295 | (2) |
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Resistance of a conducting medium |
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297 | (1) |
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On symmetry and nematic liquid crystals |
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298 | (10) |
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298 | (1) |
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The Frank free energy of nematic liquid crystals |
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298 | (2) |
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300 | (2) |
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The Freedericksz transition |
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302 | (2) |
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The twisted nematic display |
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304 | (2) |
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Fluctuations and light scattering |
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306 | (2) |
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308 | (8) |
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309 | (3) |
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312 | (2) |
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314 | (1) |
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The nematic-to-smectic-A transition |
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315 | (1) |
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Elasticity of solids: strain and elastic energy |
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316 | (14) |
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316 | (2) |
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318 | (1) |
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Isotropic and cubic solids |
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319 | (2) |
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321 | (1) |
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Mercury chain salts - one-dimensional crystals |
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322 | (2) |
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Xenon on graphite - a two-dimensional crystal |
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324 | (1) |
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Vacancies and interstitials |
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325 | (3) |
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Bond-angle order and rotational and translational elasticity |
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328 | (1) |
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Elastic constants from density functional theory |
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329 | (1) |
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330 | (4) |
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Classical theory of elasticity |
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330 | (2) |
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Elasticity of classical harmonic lattices |
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332 | (2) |
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Elasticity of solids: the stress tensor |
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334 | (7) |
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The Lagrangian stress tensor |
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334 | (3) |
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337 | (1) |
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The Eulerian stress tensor |
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338 | (3) |
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The nonlinear sigma model |
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341 | (12) |
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347 | (1) |
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347 | (1) |
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347 | (6) |
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Dynamics: correlation and response |
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353 | (64) |
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Dynamic correlation and response functions |
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354 | (5) |
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354 | (1) |
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355 | (4) |
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359 | (7) |
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359 | (1) |
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360 | (2) |
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362 | (3) |
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365 | (1) |
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Elastic waves and phonons |
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366 | (3) |
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Sound waves in an elastic continuum |
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366 | (1) |
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Acoustic phonons in a harmonic lattice |
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367 | (2) |
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369 | (12) |
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369 | (1) |
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The Green function and dynamic response |
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370 | (1) |
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371 | (2) |
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External potentials and the Einstein relation |
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373 | (2) |
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375 | (1) |
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Cooperative diffusion versus self-diffusion |
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376 | (2) |
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Master equation for diffusion on a lattice |
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378 | (3) |
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381 | (9) |
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Random forces and thermal equilibrium |
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381 | (2) |
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Correlation functions for diffusion |
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383 | (2) |
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385 | (2) |
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Fluctuation-dissipation theorem for the harmonic oscillator |
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387 | (1) |
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The Fokker-Planck and Smoluchowski equations |
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388 | (2) |
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Formal properties of response functions |
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390 | (9) |
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Response to external fields |
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390 | (2) |
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Symmetry properties of response functions |
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392 | (2) |
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394 | (1) |
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Spectral representations of χ'' ϕ |
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395 | (2) |
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The fluctuation-dissipation theorem |
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397 | (1) |
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Sum rules and moment expansions |
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398 | (1) |
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399 | (18) |
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Scattering geometry and partial cross-sections |
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399 | (1) |
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Fermi golden rule and neutron scattering |
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400 | (2) |
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The Fermi pseudopotential |
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402 | (2) |
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Coherent and incoherent scattering |
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404 | (1) |
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Cross-sections and correlation functions |
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405 | (1) |
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Neutron scattering from crystals |
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406 | (1) |
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407 | (1) |
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How neutron scattering experiments are actually done |
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408 | (2) |
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Scattering of charged particles and photons |
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410 | (1) |
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411 | (1) |
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411 | (6) |
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417 | (78) |
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Conserved and broken-symmetry variables |
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417 | (2) |
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A tutorial example - rigid rotors on a lattice |
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419 | (15) |
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420 | (1) |
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421 | (5) |
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426 | (4) |
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Excitations from the classical ground state |
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430 | (2) |
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432 | (1) |
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432 | (1) |
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433 | (1) |
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434 | (6) |
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434 | (1) |
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Generalized Heisenberg models |
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435 | (1) |
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436 | (2) |
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The isotropic antiferromagnet |
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438 | (1) |
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439 | (1) |
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Hydrodynamics of simple fluids |
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440 | (14) |
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441 | (2) |
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Thermodynamics with mass motion |
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443 | (1) |
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The entropy production equation |
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444 | (1) |
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Dissipationless hydrodynamics |
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445 | (1) |
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446 | (2) |
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The Navier-Stokes equations |
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448 | (1) |
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449 | (3) |
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452 | (1) |
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453 | (1) |
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Liquid crystals, crystalline solids, and superfluid helium |
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454 | (10) |
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454 | (2) |
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Smectic-A liquid crystals |
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456 | (3) |
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459 | (1) |
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460 | (4) |
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Stochastic models and dynamic critical phenomena |
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464 | (15) |
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Critical slowing down and the conventional theory |
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464 | (2) |
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466 | (3) |
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469 | (3) |
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472 | (3) |
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Models with Poisson brackets |
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475 | (2) |
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477 | (2) |
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Nucleation and spinodal decomposition |
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479 | (16) |
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Nucleation with a nonconserved order parameter |
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480 | (3) |
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Symmetric unstable quench with model A dynamics |
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483 | (1) |
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Conserved order parameters and spinodal decomposition |
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484 | (7) |
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491 | (1) |
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491 | (1) |
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492 | (3) |
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495 | (95) |
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Characterization of topological defects |
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495 | (11) |
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499 | (1) |
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Order parameters with more than two components |
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499 | (2) |
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Order parameter spaces and homotopy |
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501 | (5) |
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Examples of topological defects |
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506 | (20) |
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506 | (1) |
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Dislocations in smectic liquid crystals |
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507 | (5) |
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512 | (3) |
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515 | (1) |
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Hexagonal and close-packed lattices |
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515 | (2) |
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Disclinations in crystals |
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517 | (1) |
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518 | (4) |
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522 | (1) |
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522 | (2) |
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Nematic and hexatic liquid crystals |
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524 | (2) |
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Energies of vortices and dislocations |
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526 | (16) |
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Simple calculation of xy-vortex energies |
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526 | (4) |
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530 | (1) |
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Energies of dislocations in crystals |
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531 | (5) |
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Dislocations in smectic liquid crystals |
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536 | (6) |
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Vortex unbinding and the Kosterlitz-Thouless transition |
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542 | (13) |
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Vortices and the spin-wave stiffness |
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542 | (2) |
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Vortex unbinding in two dimensions - the Kosterlitz-Thouless transition |
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544 | (7) |
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551 | (4) |
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Dislocation mediated melting |
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555 | (6) |
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558 | (1) |
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Experiments and numerical simulation |
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559 | (2) |
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The twist-grain-boundary phase |
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561 | (29) |
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Structure of the TGB phase |
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561 | (3) |
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The thermodynamic critical field |
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564 | (1) |
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565 | (1) |
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566 | (2) |
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568 | (3) |
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Analogy with superconductivity |
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571 | (2) |
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Appendix 9A Notes on the Kosterlitz-Thouless transition |
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573 | (1) |
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Integration of the KT recursion relations |
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573 | (2) |
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Longitudinal and transverse response |
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575 | (2) |
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The spin correlation function |
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577 | (1) |
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Appendix 9B Duality and the Villain model |
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578 | (1) |
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579 | (3) |
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The xy-, Villain, and lattice Coulomb-gas models |
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582 | (2) |
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584 | (1) |
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584 | (1) |
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585 | (5) |
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Walls, kinks and solitons |
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590 | (72) |
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591 | (4) |
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Domain walls in mean-field theory |
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595 | (6) |
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597 | (2) |
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599 | (1) |
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599 | (2) |
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The Frenkel-Kontorowa model |
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601 | (19) |
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601 | (1) |
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602 | (1) |
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Devil's staircases and the FK phase diagram |
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603 | (2) |
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The continuum approximation |
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605 | (3) |
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608 | (2) |
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The minimum energy solution |
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610 | (3) |
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Repulsive interaction between discommensurations |
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613 | (1) |
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613 | (1) |
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Compressional elastic constants |
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614 | (1) |
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615 | (2) |
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617 | (1) |
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Extension to two dimensions |
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618 | (2) |
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620 | (15) |
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Differential geometry and the total surface area |
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620 | (3) |
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623 | (2) |
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625 | (1) |
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Fluctuations in the harmonic approximation |
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626 | (3) |
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Nonlinearities and renormalization in fluid membranes |
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629 | (1) |
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630 | (5) |
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Arrays of fluctuating walls |
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635 | (8) |
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Fluctuating walls and steric entropy |
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635 | (3) |
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Honeycomb lattice of walls |
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638 | (1) |
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Elasticity of sterically stabilized phases |
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638 | (2) |
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Dislocations and the CI transition |
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640 | (3) |
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643 | (19) |
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The solid-on-solid and discrete Gaussian models |
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643 | (3) |
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The roughening transition |
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646 | (2) |
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648 | (7) |
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655 | (1) |
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656 | (1) |
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656 | (6) |
| Glossary |
|
662 | (23) |
| Index |
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685 | |
Other versions by this Author