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arXiv · 1511.07877

Long-range order in the 3-state antiferromagnetic Potts model in high dimensions

Ohad Feldheim·Yinon Spinka
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Abstract

We prove the existence of long-range order for the 3-state Potts antiferromagnet at low temperature on $\mathbb{Z}^d$ for sufficiently large $d$. In particular, we show the existence of six extremal and ergodic infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one bipartition class have a much higher probability to be in one state than in either of the other two states. This settles the high-dimensional case of the Koteck\'y conjecture.

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Ohad Feldheim, Yinon Spinka. 2015-11-24. Long-range order in the 3-state antiferromagnetic Potts model in high dimensions. https://arxiv.org/abs/1511.07877

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