Towards a Microscopic Theory of Phase Coexistence
One of the fundamental goals of statistical mechanics is to understand the macroscopic effects induced by random forces acting at the microscopic level. We illustrate this in the context of the Ising model in the phase coexistence regime: the most likely shapes of macroscopic droplets of one pure phase floating in the other pure phase are close to the Wulff crystal of the model. Furthermore, the law of configurations at equilibrium is governed by a minimal action principle. These results come from joint works with Agoston Pisztora. We list several related open problems.
KeywordsIsing Model Gibbs Measure Large Deviation Principle Microscopic Theory Phase Coexistence
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