This tutorial will have two parts: In the first part, we will introduce basic
notions of statistical physics, including free energy, phase transitions,
critical exponents, and Gibbs measures. In the second, we will discuss the
so-called mean field approximation and show that, in the case of Ising and Potts
models on complete graphs, this approximation can be rigorously justified.
We will compare the standard notions of phase transitions in statistical
physics to these notions in graph theoretic models and problems of combinatorial