| Preface | | xi | |
| Acknowledgments | | xv | |
| Part I: Introduction | | 1 | (36) |
| | | 3 | (10) |
| What Is a Quantum Phase Transition? | | | 3 | (2) |
| Quantum Versus Classical Phase Transitions | | | 5 | (1) |
| | | 6 | (2) |
| | | 8 | (5) |
| | | 8 | (2) |
| | | 10 | (3) |
| The Mapping to Classical Statistical Mechanics: Single-Site Models | | | 13 | (15) |
| The Classical Ising Chain | | | 13 | (7) |
| | | 16 | (1) |
| | | 17 | (1) |
| Mapping to a Quantum Model: Ising Spin in a Transverse Field | | | 18 | (2) |
| The Classical X Y Chain and an O(2) Quantum Rotor | | | 20 | (6) |
| The Classical Heisenberg Chain and an O(3) Quantum Rotor | | | 26 | (2) |
| | | 28 | (9) |
| | | 30 | (3) |
| What's Different about Quantum Transitions? | | | 33 | (4) |
| Part II: Quantum Ising and Rotor Models | | 37 | (154) |
| The Ising Chain in a Transverse Field | | | 39 | (39) |
| | | 41 | (5) |
| | | 42 | (3) |
| | | 45 | (1) |
| | | 46 | (3) |
| Continuum Theory and Scaling Transformations | | | 49 | (5) |
| Equal-Time Correlations of the Order Parameter | | | 54 | (3) |
| Finite-Temperature Crossovers | | | 57 | (20) |
| Low T on the Magnetically Ordered Side, Δ > 0, T ≪ Δ | | | 59 | (6) |
| Low T on the Quantum Paramagnetic Side, Δ < 0, T ≪ |Δ| | | | 65 | (4) |
| Continuum High T, T ≫ |Δ| | | | 69 | (6) |
| | | 75 | (2) |
| Applications and Extensions | | | 77 | (1) |
| Quantum Rotor Models: Large-N Limit | | | 78 | (23) |
| | | 79 | (4) |
| | | 80 | (2) |
| | | 82 | (1) |
| Continuum Theory and Large-N Limit | | | 83 | (2) |
| | | 85 | (6) |
| Quantum Paramagnet, g > gc | | | 86 | (1) |
| | | 87 | (2) |
| Magnetically Ordered Ground State, g < gc | | | 89 | (2) |
| | | 91 | (8) |
| Low T on the Quantum Paramagnetic Side, g > gc, T ≪ Δ+ | | | 96 | (1) |
| | | 97 | (1) |
| Low T on the Magnetically Ordered Side, g < gc, T ≪ Δ- | | | 97 | (2) |
| Applications and Extensions | | | 99 | (2) |
| The d = 1, O(N ≤ 3) Rotor Models | | | 101 | (22) |
| Scaling Analysis at Zero Temperature | | | 103 | (1) |
| Low-Temperature Limit of Continuum Theory, T ≪ Δ+ | | | 104 | (6) |
| High-Temperature Limit of Continuum Theory, Δ+ ≪ T ≪ J | | | 110 | (11) |
| Field-Theoretic Renormalization Group | | | 112 | (3) |
| | | 115 | (1) |
| | | 116 | (5) |
| | | 121 | (1) |
| Applications and Extensions | | | 121 | (2) |
| The d = 2, O(N ≤ 3) Rotor Models | | | 123 | (22) |
| Low T on the Magnetically Ordered Side, T ≪ ρs | | | 125 | (9) |
| | | 126 | (3) |
| | | 129 | (2) |
| Structure of Correlations | | | 131 | (3) |
| Dynamics of the Quantum Paramagnetic and High-T Regions | | | 134 | (9) |
| | | 136 | (4) |
| | | 140 | (3) |
| | | 143 | (1) |
| Applications and Extensions | | | 144 | (1) |
| Physics Close to and above the Upper-Critical Dimension | | | 145 | (23) |
| | | 147 | (4) |
| | | 147 | (2) |
| | | 149 | (1) |
| Field-Theoretic Renormalization Group | | | 150 | (1) |
| Statics at Nonzero Temperatures | | | 151 | (8) |
| | | 153 | (4) |
| | | 157 | (2) |
| Order Parameter Dynamics in d = 2 | | | 159 | (6) |
| Applications and Extensions | | | 165 | (3) |
| | | 168 | (23) |
| | | 172 | (4) |
| | | 175 | (1) |
| | | 176 | (1) |
| Collisionless Transport Equations | | | 176 | (4) |
| Collision-Dominated Transport | | | 180 | (8) |
| | | 180 | (5) |
| | | 185 | (3) |
| | | 188 | (1) |
| Applications and Extensions | | | 189 | (2) |
| Part III: Other Models | | 191 | (144) |
| | | 193 | (10) |
| | | 195 | (3) |
| Continuum Quantum Field Theories | | | 198 | (3) |
| Applications and Extensions | | | 201 | (2) |
| Dilute Fermi and Bose Gases | | | 203 | (26) |
| | | 205 | (2) |
| The Dilute Spinless Fermi Gas | | | 207 | (7) |
| Dilute Classical Gas, T ≪ |μ|, μ < 0 | | | 209 | (1) |
| Fermi Liquid, kBT ≪ μ, μ > 0 | | | 210 | (3) |
| | | 213 | (1) |
| | | 214 | (8) |
| | | 216 | (2) |
| | | 218 | (4) |
| Correlators of ZB in d = 1 | | | 222 | (6) |
| Dilute Classical Gas, T ≪ |μ|, μ < 0 | | | 223 | (2) |
| Tomonaga-Luttinger Liquid, T ≪ μ, μ > 0 | | | 225 | (1) |
| | | 226 | (1) |
| | | 227 | (1) |
| Applications and Extensions | | | 228 | (1) |
| Phase Transitions of Fermi Liquids | | | 229 | (11) |
| | | 230 | (4) |
| Finite-Temperature Crossovers | | | 234 | (4) |
| Applications and Extensions | | | 238 | (2) |
| Heisenberg Spins: Ferromagnets and Antiferromagnets | | | 240 | (34) |
| Coherent State Path Integral | | | 240 | (5) |
| | | 245 | (5) |
| | | 250 | (15) |
| | | 251 | (9) |
| Noncollinear Ordering and Deconfined Spinons | | | 260 | (5) |
| Partial Polarization and Canted States | | | 265 | (7) |
| | | 267 | (1) |
| | | 268 | (1) |
| | | 268 | (2) |
| Zero Temperature Critical Properties | | | 270 | (2) |
| Applications and Extensions | | | 272 | (2) |
| Spin Chains: Bosonization | | | 274 | (24) |
| The X X Chain Revisited: Bosonization | | | 275 | (8) |
| | | 283 | (12) |
| | | 286 | (1) |
| Tomonaga-Luttinger Liquid | | | 287 | (1) |
| | | 288 | (3) |
| | | 291 | (1) |
| Models with SU (2) (Heisenberg) Symmetry | | | 292 | (2) |
| Critical Properties near Phase Boundaries | | | 294 | (1) |
| O(2) Rotor Model in d = 1 | | | 295 | (1) |
| Applications and Extensions | | | 296 | (2) |
| Magnetic Ordering Transitions of Disordered Systems | | | 298 | (22) |
| | | | |
| Stability of Quantum Critical Points in Disordered Systems | | | 299 | (1) |
| Griffiths--McCoy Singularities | | | 300 | (3) |
| Perturbative Field-Theoretic Analysis | | | 303 | (3) |
| | | 305 | (1) |
| Quantum Ising Models Near the Percolation Transition | | | 306 | (5) |
| | | 306 | (1) |
| Classical Dilute Ising Models | | | 307 | (1) |
| Quantum Dilute Ising Models | | | 308 | (3) |
| The Disordered Quantum Ising Chain | | | 311 | (7) |
| | | 318 | (1) |
| Applications and Extensions | | | 319 | (1) |
| | | 320 | (15) |
| | | 321 | (5) |
| | | 325 | (1) |
| | | 326 | (7) |
| Applications and Extensions | | | 333 | (2) |
| References | | 335 | (14) |
| Index | | 349 | |
