Syllabus

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