Statistical Quantum Field Theory 1

The course gives a theoretical introduction to the problem of phase transitions in statistical mechanics and to Renormalziation Group. In particular
It is considered the Ising model, the Onsager exact solution, the non gaussian fermion and
Boson functional integrals, the symmetry breaking, the critical phenomena, the Wilsonian Renormalization Group , the notion of universality, the vertex and dimer models, the phi4 model in several dimensions.

At the end the student will know the concepts of Phase Transitions and Renormalization Group, and he will be able for instance
1)to compute the correlations and the free energy of the Ising model in one dimension
2)To prove the phase transition in the infinite range Ising model
3)To compute the critical temperature in the Ising model in 2 dimensions and some critical exponents using Onsager solution
4)To compute correlations in the dimer model
5) To write the Feynman graph expansion in certain models
6) To compute the scaling dimensions in the RG sense and to say if they are relevant irrelevant or marginal
7)To compute the perturbative corrections to the critical temperature in models like next to nearest neighbor Ising model.