| Preface | p. ix |
| A few well-known basic results | p. 1 |
| The Boltzmann law | p. 1 |
| The classical canonical ensemble | p. 1 |
| The quantum canonical ensemble | p. 2 |
| The grand canonical ensemble | p. 3 |
| Thermodynamics from statistical physics | p. 3 |
| The thermodynamic limit | p. 3 |
| Gaussian integrals and Wick's theorem | p. 4 |
| Functional derivatives | p. 6 |
| d-dimensional integrals | p. 6 |
| Additional references | p. 8 |
| Introduction: order parameters, broken symmetries | p. 9 |
| Can statistical mechanics be used to describe phase transitions? | p. 9 |
| The order-disorder competition | p. 10 |
| Order parameter, symmetry and broken symmetry | p. 12 |
| More general symmetries | p. 16 |
| Characterization of a phase transition through correlations | p. 18 |
| Phase coexistence, critical points, critical exponents | p. 19 |
| Examples of physical situations modelled by the Ising model | p. 22 |
| Heisenberg's exchange forces | p. 22 |
| Heisenberg and Ising Hamiltonians | p. 24 |
| Lattice gas | p. 26 |
| More examples | p. 28 |
| A first connection with field theory | p. 29 |
| A few results for the Ising model | p. 32 |
| One-dimensional Ising model: transfer matrix | p. 32 |
| One-dimensional Ising model: correlation functions | p. 35 |
| Absence of phase transition in one dimension | p. 37 |
| A glance at the two-dimensional Ising model | p. 38 |
| Proof of broken symmetry in two dimensions (and more) | p. 38 |
| Correlation inequalities | p. 42 |
| Lower critical dimension: heuristic approach | p. 44 |
| Digression: Feynman path integrals, the transfer matrix and the Schrödinger equation | p. 47 |
| High-temperature and low-temperature expansions | p. 52 |
| High-temperature expansion for the Ising model | p. 52 |
| Continuous symmetry | p. 55 |
| Low-temperature expansion | p. 56 |
| Kramers-Wannier duality | p. 57 |
| Low-temperature expansion for a continuous symmetry group | p. 58 |
| Some geometric problems related to phase transitions | p. 60 |
| Polymers and self-avoiding walks | p. 60 |
| Potts model and percolation | p. 64 |
| Phenomenological description of critical behaviour | p. 68 |
| Landau theory | p. 68 |
| Landau theory near the critical point: homogeneous case | p. 71 |
| Landau theory and spatial correlations | p. 75 |
| Transitions without symmetry breaking: the liquid-gas transition | p. 78 |
| Thermodynamic meaning of (m) | p. 79 |
| Universality | p. 80 |
| Scaling laws | p. 82 |
| Mean field theory | p. 85 |
| Weiss 'molecular field' | p. 85 |
| Mean field theory: the variational method | p. 87 |
| A simpler alternative approach | p. 92 |
| Beyond the mean field theory | p. 95 |
| The first correction to the mean-field free energy | p. 95 |
| Physical consequences | p. 97 |
| Introduction to the renormalization group | p. 100 |
| Renormalized theories and critical points | p. 101 |
| Kadanoff block spins | p. 101 |
| Examples of real space renormalization groups: 'decimation' | p. 103 |
| Structure of the renormalization group equations | p. 109 |
| Renormalization group for the 4 theory | p. 113 |
| Renormalization group … without renormalization | p. 114 |
| Study of the renormalization group flow in dimension four | p. 116 |
| Critical behaviour of the susceptibility in dimension four | p. 118 |
| Multi-component order parameters | p. 120 |
| Epsilon expansion | p. 122 |
| An exercise on the renormalization group: the cubic fixed point | p. 125 |
| Renormalized theory | p. 128 |
| The meaning of renormalizability | p. 128 |
| Renormalization of the massless theory | p. 132 |
| The renormalized critical free energy (at one-loop order) | p. 134 |
| Away from Tc | p. 136 |
| Goldstone modes | p. 138 |
| Broken symmetries and massless modes | p. 138 |
| Linear and non-linear O(n) sigma models | p. 142 |
| Regularization and renormalization of the O(n) non-linear sigma model in two dimensions | p. 144 |
| Regularization | p. 144 |
| Perturbation expansion and renormalization | p. 148 |
| Renormalization group equations for the O(n) non-linear sigma model and the (d - 2) expansion | p. 150 |
| Integration of RG equations and scaling | p. 151 |
| Extensions to other non-linear sigma models | p. 153 |
| Large n | p. 156 |
| The linear O(n) model | p. 156 |
| O(n) sigma model | p. 161 |
| Index | p. 165 |
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