Preface
1 Introduction
1.1 Phase transitions and order parameters
1.2 Models: Ising, XY, Heisenberg
1.3 Universality and critical exponents
1.4 Scaling of free energy
1.5 Correlations and hyperscaling
2 Ginzburg-Landau-Wilson theory
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 Renormalization group
3.1 Idea
3.2 Momentum-shell transformation
3.3 E-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 Superconducting transition
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 σ-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 Universal jump of superfluid density
6.6 Heisenberg model
7 Duality in 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 ~4-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
