A Personal List of Unsolved Problems Concerning Lattice Gases and Antiferromagnetic Potts Models

Details A Personal List of Unsolved Problems Concerning Lattice Gases and Antiferromagnetic Potts Models A Personal List of Unsolved Problems Concerning Lattice Gases and Antiferromagnetic Potts Models

2000-04-13

arxiv.org/abs/cond-mat/0004231v3

Markov Process. Related Fields 7, 21-38 (2001)

Physics

Condensed Matter

Statistical Mechanics

19 pages, LaTeX2e. Talk presented at the conference on Inhomogeneous Random Systems, Universit\'e de Cergy-Pontoise, 25 Januar

Scientific paper

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.

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