Two-dimensional Statistical mechanics
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
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.)