Combinatorial Methods for Statistical Physics Models

Special Topics Course, Winter 1999

Many fundamental questions in statistical mechanics are inherently combinatorial. We will introduce some basic models and examine natural physical questions from a combinatorial perspective, including the Ising model, the Potts model, monomer-dimer systems, self-avoiding walks and percolation theory. Some highlights of the course will include the Peierls argument (for the Ising model), Kasteleyn's theorem (for dimer systems), the FKG inequality, and Reimer's new generalization of the BK inequality (both used in percolation theory).

This course is intended to be introductory and no background in statistical mechanics is required.

Time: Tuesday and Thursday 2-3:30 (tentatively).

Prerequisites: Some background in combinatorics and probability.

Text: None.

Some references:

Lecture Notes: