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Goldenfeld N. — Lectures on Phase Transitions and the Renormalization Group
Goldenfeld N. — Lectures on Phase Transitions and the Renormalization Group

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Название: Lectures on Phase Transitions and the Renormalization Group

Автор: Goldenfeld N.

Аннотация:

Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level. Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.


Язык: en

Рубрика: Физика/Термодинамика, статистическая физика/Квантовые методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 394

Добавлена в каталог: 06.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Amplitude ratio      132
Anisotropic exchange      274
Anomalous dimension      195 208 287
Anomalous dimension and solvability conditions      299
Anomalous dimension in PDEs      293
Anomalous dimension, consequence of renormalisation      309
Anomalous dimension, heuristic calculation      305
Anomalous dimension, occurence in linear problem      333
Anomalous pairing amplitude      137
Antiferromagnet      10 268
Approach to equilibrium      19 216 219
Assumption of renormalisability      313
asymptotic freedom      313
Asymptotic series      192 313
Atomic bomb      20
Auxiliary fields      82
Ballistic deposition      217
Barenblatt’s equation      296 357
Basin of attraction      241—243
Baxter model      32
Binary alloy      19
Binary fluid mixture      13
Bipartite      42
Block copolymers      224
Block spin transformation      231
Boiling      119
Boltzmann distribution      52
Borel summation      192 352
boundary conditions      24
Brownian motion      46 211
Bulk free energy density      25
Cahn — Hilliard equation      223
Characteristic equations      330
Characteristics      317
Classical spinodal      220 221
Clausius — Clapeyron relation      118
Coarse-grained Hamiltonian      237 259
Coarse-grained order parameter      148
Coarse-graining      230
Coarse-graining, generation of new interactions by      376
Codimension      29 140 171 243 246
Coexistence curve      7 220
Common sense      196 291
Compressibility      120 122 126 128 129
Configurational sum      73
Confluent singularity      132 279
Continuity fixed point      247
Continuous symmetry      54 335
continuum limit      154
Convexity      36—38
Cooper pair      137
Corrections to scaling      131 279 314
Correlation function      95 128 129 159 160 167 168 179 195 208 212 234 270
Correlation function, dimensional analysis of      193
Correlation function, longitudinal      337
Correlation function, scaling hypothesis for      206
Correlation function, transverse      337
correlation length      31 98 110
Coulomb’s law      26
Coupling constants      24
Critical exponents      8
Critical exponents, definition of      131
Critical exponents, difficulties in determination of      132 273
Critical exponents, non-universal      80
Critical exponents, table of values      111
Critical fixed point      243
Critical isotherm      107 205
Critical manifold      243 248
Critical point      7 119 247
Critical region      170
Critical slowing down      133 212
Crossover exponent      275 284 383
Crossover phenomena      185 271 383
Cubic anisotropy      276
Cumulant      373
Cumulant expansion      260 302 363
Cusp      11 279
Dangerous irrelevant variable      254 278 283 359 360
Data collapse      203
Debye screening length      27
Degeneracy      101
Delta function      155
Differential RG transformation      256 354 357
Diffusion equation      289
Dilation parameter      331
Dimensional analysis      6 8 19 20 288
Dimensionality      18 45 170
Disconnected diagram      373
Discontinuity      108
Discontinuity fixed point      247 267 269
Discrete symmetry      54
Discretisation      177
Disorder      59
Disorder, annealed      69
Disorder, quenched      68 276
Divergence      11 183 302
Divergence of perturbation theory      192
Divergence of perturbation theory, origin of      303
Don-symmetric      265
Drosophila      23
Dynamic critical phenomena      134
Dynamic scaling hypothesis      213
Dynamical seeding      202
Dynamical systems      24
Dyson’s argument      192 313 323
D’arcy’s Law      294
Early Universe      336
Effective Hamiltonian      149 231 237 259
Ehrenfest classification      14 172
Eight-vertex model      80
Einstein summation convention      175 244 340
Electromagnetic penetration depth      342
Electroweak theory      316 342
Energy-entropy argument      43 349
Equilibrium amorphous solid      62
Equilibrium volume      120
Equipartition of energy      179 340
EQUIVALENCE      74 79
Ergodic hypothesis      56
Ergodicity breaking      57 58
exchange interaction      34
Excluded volume      123
Exclusion principle      27
expansion      18 1
Expansion, cumulant      302
Expansion, e      18 351
Expansion, n      18 168
Expansion, perturbation      323
External leg      370
F model      32
Fermion      27
Ferromagnet      9
Ferromagnetic fixed point      266 269
Feynman diagram      370
Field theory      157 197 303 313 342 385
Fine structure constant      313
Finite size effect      31 133
Finite size scaling      279
Finite time blow-up      328
Fixed point hamiltonian      243 305
Fixed points      241 242
Fluctuation      135 175
Fluctuation dissipation theorem      209
Fluctuation-dissipation theorem      211
Fluctuation-induced first order transition      147
Fluctuations      17 174
Fluid mechanics      19
Fokker — Planck equation      211 226
Fourier transform      155 212
Free energy      15 25
Free energy, Cahn — Hilliard      222
Free energy, coarse-grained      149
Free energy, Gibbs      118 138 140 149 163
Free energy, grand      73
Free energy, Helmholtz      118 139
Free energy, Landau      140 163
Free energy, scaling hypothesis for      206
Free field theory      174
Frustration      42
Fugacity      73
Functional      146 149 157
Functional derivative      157
Functional derivative, definition      157
Functional integral      115 152—154 186 288 303
Functional integral, measure      155
Gap exponent      203 359
Gaussian approximation      173 174 345
Gaussian approximation in ordered state      340
Gaussian fixed point      353 360
Gaussian model      354
Gaussian random function      210 277
Generalised isothermal susceptibility      157
Generating function      157
Geometry      20
Gibbs      15
Ginzburg criterion      169 175 185 355 360
Ginzburg — Landau theory      153 216
Goldstone mode      342
Goldstone modes      340
Goldstone’s theorem      335
Gram — Schmidt orthogonalisation      255
Grand free energy      73
Grand potential      73
Gravity      27
Green function      159 289
Hamilton      15
Hard spins      346
Harris criterion      276 278
heat capacity      11 126
Heat capacity at constant pressure      126
Heaviside function      227 303
Heisenberg model      32 54 267 336
Heisenberg model, effects of anisotropy      274
Helium      11 119 137 164 172 350
Holder inequality      39
Homogeneous nucleation      220
Hubbard-Stratonovich transformation      82 153 186 353
Hyperscaling      207
Iceberg      16
Infinite-range Ising spin glass      68
Infra-red divergence      183 345 351
Initial conditions      45
Instrumental resolution      133
Integral surface      329
INTERFACE      19
Interface, growth      19 217
Intermediate asymptotics      218 221 292
Intermediate asymptotics, first kind      292 301
Intermediate asymptotics, second kind      301
Intermediate vector bosons      342
Internal energy      43
Internal line      371
Internal momentum      371
Invariant      29
Invariant manifold      265
Inverse square law      26
Irrelevant eigenvalue      246
Irrelevant variables      254
Ising model      9 32 54 111
Ising model, crossover to      274
Isothermal susceptibility      204
Jacobian      128
Josephson scaling law      202 207 251
Kadanoff      18 230
Kepler’s law      5
Kosterlitz — Thouless transition      137 335 378
KPZ equation      219 288
Kramers — Kronig relations      214
Lagrangian      336
Lambda transition      11 172
Landau free energy      140 315
Landau theory      17 108 112 140
Landau theory for O(n) model      336
Landau theory, microscopic      153 162
Landau theory, microscopic interpretation      169
Landau theory, phenomenological      153 315
Landau theory, self-consistency      167
Langevin equation      210 218 288
Latent heat      14 119
LATEX      62
Lattice derivatives      177
Lattice gas      74 111 216
Law of corresponding states      17 125 134
Left eigenvectors      244 255
Level crossing      44
Linearis'd RG transformation      255
Linearised RG matrix      244
Linked cluster theorem      374 375 385 387
Liquid crystals      147 336
Local magnetisation      147
Local operators      24
Logarithmic corrections      170
Logarithmic divergence      131 352
London equation      215
Long range order      45 48 98 104 335 339 343 347
Longitudinal correlation function      337
Loop expansion      186
Low temperature expansion      85 101
Lower critical dimension      45 344 346 384
Lower critical dimension, continuous symmetry      345
Lower critical dimension, discrete symmetry      49
Magnetic dipoles      9
Magnetisation      18 45
Magnetisation, definition      45
Majority rule      258
Marginal eigenvalue      246
Maxwell’s equal area rule      121
Maxwell’s equal area rule, magnetic systems      164
Mean field theory      17 69 85 104 123 135
Mechanical equilibrium      121
Mermin — Wagner theorem      55 345
Metastability      121 220
Method of characteristics      317 329
Method of sources      34
Minimal model      12 33 62 328
Modified Bessel function      161
Modified porous medium equation      295 304 333
Modulated phases      165
Momentum shell RG      351
Monomers      62
Monte Carlo simulation      279
Multicritical point      247
Multiple phase coexistence      247
Neural network      71
Nienhuis — Nauenberg criterion      269
Noise      210
Non-equilibrium phenomena      18
Non-equilibrium steady state      216
Non-equilibrium systems      202
Non-linear diffusion      287
Non-linear eigenvalue      299
Non-linear response function      214
Non-linear sigma model      32
Non-symmetric matrices      244 255
Notation      6 35 146 155 190 210 236 336 362
Nucleation      220
Ohm’s Law      13
Order of a transition      147
Order parameter      9 18 65 136
Order parameter, number of components of      136 173
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