1.      First and second order phase transitions, order parameter, correlation functions, critical exponents, simple models. 

2.      Mean field theory: (a) for the order parameter (b) for the correlation function.

3.      Fluctuations of the order parameter, Levanyuk-Ginzburg criterion. General idea of scaling. Exactly solvable models: 2d Ising model 

4.      The idea of renormalization: (a) Block spins (b) One dimensional Ising model (c) The structure of the general theory, beta functions, relevant and irrelevant variables, scaling of the free energy and derivation of scaling relations.  Phase diagrams, fixed points and crossover, scaling operators and scaling dimensions  

5.      Epsilon expansion, 4d continuous Ising model, simple diagrams, marginal variables.

6.      Low dimensional systems, Mermin-Wagner-Hohenberg theorem, Berezinskii-Kosterlitz-Thouless transition.

7.      Random systems, replica trick, Haris criterion. random fields.

8.      Critical dynamics, Gaussian and discrete models, dynamical scaling, response functional.

9.      Brief introduction to quantum phase transitions.

Bibliography

John Cardy-”Scaling and Renormalization in Statistical Physics” ,Cambridge Lecture notes in Physics, Cambridge University Press.

Nigel Goldenfeld-“Lectures on Phase Transitions and the Renormalization group”, Frontiers in Physics, vol. 85.