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On the Gibbs states of the Ising and Potts models

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I will first review what is known about the set of Gibbs states of the Ising and Potts models, mentioning recent joint work with H. Duminil-Copin, D. Ioffe and Y. Velenik for the 2d case. A natural question (open in general) is to determine whether any Gibbs state is weak limit of finite-volume measures with deterministic boundary conditions. I will give a counter-example in the 3d Ising case, and point out what the issues are in order to extend it to the Potts model. I’ll end with a few conjectures.

This talk is part of the Probability series.

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