Math 2720: Statistical Mechanics and Combinatorics

Professor Richard Kenyon
Tel. 863-6406
rkenyon -at- math dot brown dot edu
office: 305 Kassar
Office hours: TBA

R. Baxter, Exactly solved models in statistical mechanics (Dover books on physics) here
R. Kenyon, "Lectures on dimers" here
N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating sign matrices and domino tilings, J. Algebraic Combin. 1 (1992), 111–132 and 219–234.(arxiv:math/ 9201305)
Wikipedia pages: Maxwell-Boltzmann statistics, Ising model, ice-type model, ...

Apr 14,16: instead of class, go to the lectures of Smart (Tues) and Bodineau (Thurs)

Course outline: After a brief introduction to statistical mechanical concepts, we'll study combinatorial and probabilistic aspects of the classical lattice models (Ising model, dimer model, spanning tree model, 6-vertex model). The subjects covered will be subject to the interests of the participants.


Homework 1 Due Feb 19.
HW 1, problem 3 write up by Xufan Zhang
Homework 2 Due March 10.
Homework 3 Due March 24.
Homework 4 Due April 14.
Homework 5 Due May 12.

Lecture notes (by Ren Yi)

Lecture 1
Lecture 2 (updated March 10)
Lecture 3
Lecture 4
Lecture 5
Lecture 6