Phase Transitions and Critical Phenomena

General Introduction: Origin of phase transition, thermodynamic instabilites, Maxwell construction. Classification of phase transitions: first order and second order. Phase transitions in different systems (e.g. liquid-gas and paramagnet-ferromagnetic transition), order parameter, critical exponents, concept of long-range order.

Lattice models: Ising Model, exact solution in one dimension, high-temperature and low-temperature expansions. Phase transitions in X-Y and Heisenberg Models.

Mean field theory and Landau theory. Landau-Ginzburg theory for fluctutations. Sponteneous symmetry breaking, Introduction to Mermin-Wagner theorem.

  Quasi-long-range order, Kosterlitz-Thouless transition. Renormalization Group: scaling hypothesis and        universality, renormalization group transformation. Upper and lower critical dimensions, epsilon-expansion.

Introduction to nonequilibrium Statistical Mechanics. Markov Processes, Master equation, Langevin Equation.

1. M. Plischke and B. Bergersen, Equilibrium Statistical Physics.

2. J. Cardy, Scaling and Renormalization in Statistical Physics.

3. R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics.

4. S-K Ma, Statistical Mechanics, World Scientific.

Same as References