| Preface 1 Collective behavior， from particles to fields 1.1 Introduction 1.2 Phonons and elasticity 1.3 Phase transitions 1.4 Critical behavior Problems 2 Statistical fields 2.1 Introduction 2.2 The Landau-Ginzburg Hamiltonian 2.3 Saddle point approximation， and mean-field theory 2.4 Continuous symmetry breaking and Goldstone modes 2.5 Discrete symmetry breaking and domain walls Problems 3 Fluctuations 3.1 Scattering and fluctuations 3.2 Correlation functions and susceptibilities 3.3 Lower critical dimension 3.4 Comparison to experiments 3.5 Gaussian integrals 3.6 Fluctuation corrections to the saddle point 3.7 The Ginzburg criterion Problems 4 The scaling hypothesis 4.1 The homogeneity assumption 4.2 Divergence of the correlation length 4.3 Critical correlation functions and self-similarity 4.4 The renormalization group （conceptual） 4.5 The renormalization group （formal） 4.6 The Gaussian model （direct solution） 4.7 The Gaussian model （renormalization group） Problems 5 Perturbative renormalizafion group 5.1 Expectation values in the Gaussian model 5.2 Expectation values in perturbation theory 5.3 Diagrammatic representation of perturbation theory 5.4 Susceptibility 5.5 Perturbative RG （first order） 5.6 Perturbative RG （second order） 5.7 The e-expansion 5.8 Irrelevance of other interactions 5.9 Comments on the e-expansion Problems 6 Lattice systems 6.1 Models and methods 6.2 Transfer matrices 6.3 Position space RG in one dimension 6.4 The Niemeijer-van Leeuwen cumulant approximation 6.5 The Migdal-Kadanoff bond moving approximation 6.6 Monte Carlo simulations Problems 7 Series expansions 7.1 Low-temperature expansions 7.2 High-temperature expansions 7.3 Exact solution of the one-dimensional Ising model 7.4 Self-duality in the two-dimensional Ising model 7.5 Dual of the three-dimensional Ising model 7.6 Summing over phantom loops 7.7 Exact free energy of the square lattice Ising model 7.8 Critical behavior of the two-dimensional Ising model Problems 8 Beyond spin waves 8.1 The nonlinear tr model 8.2 Topological defects in the XY model 8.3 Renormalization group for the Coulomb gas 8.4 Two-dimensional solids 8.5 Two-dimensional melting Problems 9 Dissipative dynamics 9.1 Brownian motion of a particle 9.2 Equilibrium dynamics of a field 9.3 Dynamics of a conserved field 9.4 Generic scale invariance in equilibrium systems 9.5 Non-equilibrium dynamics of open systems 9.6 Dynamics of a growing surface 10 Directed paths in random media 10.1 Introduction 10.2 High-T expansions for the random-bond Ising model 10.3 The one-dimensional chain 10.4 Directed paths and the transfer matrix 10.5 Moments of the correlation function 10.6 The probability distribution in two dimensions 10.7 Higher dimensions 10.8 Random signs 10.9 Other realizations of DPRM 10.10 Quantum interference of strongly localized electrons 10.11 The locator expansion and forward scattering paths 10.12 Magnetic field response 10.13 Unitary propagation 10.14 Unitary averages Solutions to selected problems Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Index |
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