Topics in Statistical Physics and Probability Theory (0366-5059)

Spring 2017, Tel Aviv University

Location: Schreiber 209, Tuesdays 10-13

Instructor: Ron Peled

The course is an introduction to the mathematical theory of Statistical Physics.


Statistical Physics focuses on understanding the macroscopic properties of a material from the point of view of its constituent microscopic particles. The theory focuses on the understanding of phase transitions, dramatic changes in the macroscopic properties occuring as a result of small changes in the outside parameters - such as the boiling of water at 100 degrees Celsius or the spontaneous magnetization of metals at low temperature. The course focuses on the mathematical theory of statistical physics, based on probability theory, through the consideration of several basic models. Among the models considered are the Ising model, the spin O(n) and loop O(n) models and random surfaces. Time permitting, we will discuss additional models including spatial random permutations, the quantum Heisenberg model and anti-ferromagnetic models.

No background in physics is required. We will make use of probability theory as taught in Probability for Mathematicians or Probability for the Sciences. It is possible to study Probability for Mathematicians in parallel to the course.

In some of the topics we will follow the excellent book of Friedli and Velenik.
We will also make use of the following lecture notes on the spin and loop O(n) models, and possibly also of the following lecture notes on spatial random permutations.

As further reference, the notes of Roland Bauerschmidt are recommended.


Homework exercise 1. To be handed in by April 25 in class.

A brief overview of infinite-volume Gibbs measures.

Homework exercise 2. To be handed in by July 10 to the instructor's mailbox.