Preface ........................................................ xi
Part I Near-equilibrium critical dynamics
Introduction .................................................... 3
1 Equilibrium critical phenomena ............................... 5
1.1 Mean-field theory ....................................... 6
1.2 Landau-Ginzburg theory ................................. 16
1.3 Scaling theory ......................................... 23
1.4 Momentum shell renormalization group ................... 28
1.5 Appendix: Functional derivatives and integration ....... 39
Problems .................................................... 41
2 Stochastic dynamics ......................................... 45
2.1 Dynamic response and correlation functions ............. 46
2.2 Stochastic processes ................................... 56
2.3 Three examples ......................................... 67
2.4 Langevin equations ..................................... 77
Problems .................................................... 92
3 Dynamic scaling ............................................. 96
3.1 Dynamic scaling hypothesis ............................. 97
3.2 Continuum theory:relaxational models .................. 101
3.3 Conserved quantities and reversible mode couplings .... 112
Problems ................................................... 126
4 Dynamic perturbation theory ................................ 130
4.1 Response field formalism .............................. 131
4.2 Relaxational dynamics: systematic perturbation
theory ................................................ 135
4.3 Feynman diagrams ...................................... 142
4.4 Vertex functions ...................................... 153
4.5 Appendix: discretization, Jacobian, and response
loops ................................................. 167
Problems ................................................... 168
5 Dynamic renormalization group .............................. 171
5.1 Primitive divergences and scaling dimensions .......... 172
5.2 Renormalization via dimensional regularization ........ 177
5.3 Renormalization group and dimensional expansion ....... 185
5.4 Broken rotational symmetry and Goldstone modes ........ 193
5.5 Appendix: integrals in dimensional regularization ..... 202
Problems ................................................... 204
6 Hydrodynamic modes and reversible mode couplings ........... 207
6.1 Coupling to a conserved scalar field .................. 208
6.2 Reversible mode couplings in isotropic ferromagnets ... 217
6.3 The O(n)-symmetric Sasvári-Schwabl-Szépfalusy model ... 226
6.4 Critical dynamics of binary fluids .................... 238
Problems ................................................... 246
7 Phase transitions in quantum systems ....................... 251
7.1 Coherent-state path integrals ......................... 252
7.2 Boson superfluids ..................................... 266
7.3 Quantum critical phenomena ............................ 283
7.4 Quantum antiferromagnets .............................. 290
7.5 Appendix: Matsubara frequency sums .................... 301
Problems ................................................... 301
Part II Scale invariance in non-equilibrium systems
Introduction .................................................. 307
8 Non-equilibrium critical dynamics .......................... 309
8.1 Non-equilibrium critical relaxation and 'aging' ....... 310
8.2 Coarsening and phase ordering ......................... 319
8.3 Effects of violating the detailed balance conditions .. 329
8.4 Non-equilibrium work and fluctuation theorems ......... 336
8.5 Appendix: general Gaussian fluctuations ............... 339
Problems ................................................... 341
9 Reaction-diffusion systems ................................. 345
9.1 Rate equations and scaling theory ..................... 346
9.2 Field theory for stochastic interacting particle
systems ............................................... 355
9.3 Diffusion-limited annihilation: depletion zones ....... 367
9.4 Pair annihilation of distinct particle species ........ 376
9.5 Fluctuation effects in two-species binary reactions ... 382
Problems ................................................... 394
10 Active to absorbing state transitions ...................... 400
10.1 The directed percolation universality class ........... 401
10.2 DP variants and other percolation processes ........... 412
10.3 Branching and annihilating random walks ............... 426
Problems ................................................... 437
11 Driven diffusive systems and growing interfaces ............ 443
11.1 Driven diffusive systems .............................. 444
11.2 Critical dynamics of driven Ising lattice gases ....... 456
11.3 Driven interfaces and the KPZ equation ................ 469
11.4 Renormalization group analysis of the KPZ equation .... 479
Problems ...................................................... 492
Index ......................................................... 499
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