Preface 1 Introduction 1.1 Phase transitions and order parameters 1.2 Models: Ising,XY,Heisenberg 1.3 Universality and criticalexponents 1.4 Scaling of free energy 1.5 Correlations and hyperscaling 2 Ginzburg—Landau—Wilsontheory 2.1 Partition function for interacting bosons 2.2 Bose—Einstein condensation 2.3 Hartree approximation 2.4 Landau's mean—field theory 2.5 Upper critical dimension 3 Renormalizationgroup 3.1 Idea 3.2 Momentum—shelltransformation 3.3 ε—expansion 3.4 Dangerously irrelevant coupling 3.5 Corrections to scaling 3.6 Field—theoretic perspective 3.7 Computation of anomalous dimension 3.8 Summary 4 Superconductingtransition 4.1 Meissner effect 4.2 Fluctuation—induced first—order transition 4.3 Type—II superconductors near four dimensions 4.4 Anomalous dimension for the gauge field 4.5 Width of the critical region 5 Near lower critical dimension 5.1 Goldstone modes 5.2 Mermin—Wagner—Hohenberg theorem 5.3 Non—linear cr—model 5.4 Low—temperature expansion 5.5 Discussion 6 Kosterlitz—Thouless transition 6.1 Vortices and spin waves 6.2 Mean—field theory 6.3 Duality and the sine—Gordon theory 6.4 Renormalization of the sine—Gordon model 6.5 Universaljump of superfluid density 6.6 Heisenberg model 7 Dualityin higher dimensions 7.1 Frozen lattice superconductor 7.2 Confinement of magnetic monopoles 7.3 Magnetic field correlations 7.4 Compact electrodynamics 8 Quantum phase transitions 8.1 Dynamical critical exponent 8.2 Quantum critical point in φ4—theory 8.3 Bose—Hubbard model 8.4 Quantum fluctuations and the superfluid density 8.5 Universal conductivity in two dimensions Appendix A Hubbard—Stratonovich transformation Appendix B Linked—cluster theorem Appendix C Gauge fixing for long—range order Select bibliography Index