Two-dimensional Statistical mechanics

Math 2720
Instructor: Richard Kenyon

rkenyon -at- math dot brown dot edu

office hours: Fridays 2-5pm

In this course we will introduce a few of the basic concepts of equilibrium statistical mechanics, including Boltzmann disctributions and Gibbs measures, and then discuss simple lattice models (Ising, dimer, Potts and others). The bulk of the course will cover the dimer model and its relation to random interfaces, along with recent solutions to the limit shape problem for stepped surfaces.

There are no prerequisites, although some knowledge of elementary probability will be helpful. We will attempt to give background whenever necessary.

The course will be an expanded version of lectures I gave at Park City in 2007. Lecture notes for that course are available here.

No class Friday March 21

Homework 1 due Feb 14.
Homework 2 due Feb 27: do exercises 2,3,5,7,10,11 of the lecture notes.
Homework 3 due Apr 2: do exercises 13,14,15,17 of the lecture notes.
Homework 4 due May 12: do exercises 19,20,21 of the lecture notes. (Note: the numbering of the exercises may have changed; use the current version of the notes for this assignment)
(Exercise 19 hint: show that the frozen boundary is tangent to the sides of a hexagon, and z has the correct values there.)