- 00-219 Alan D. Sokal
- A personal list of unsolved problems concerning Potts models and
May 10, 00
(auto. generated ps),
of related papers
Abstract. I review recent results and unsolved problems
concerning the hard-core lattice gas and the q-coloring model
(antiferromagnetic Potts model at zero temperature).
For each model, I consider its equilibrium properties
(uniqueness/nonuniqueness of the infinite-volume Gibbs measure,
complex zeros of the partition function)
and the dynamics of local and nonlocal Monte Carlo algorithms
(ergodicity, rapid mixing, mixing at complex fugacity).
These problems touch on mathematical physics, probability,
combinatorics and theoretical computer science.