Journal of the European Mathematical Society
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Published online: 2019-02-01
Long-range order in the 3-state antiferromagnetic Potts model in high dimensionsOhad N. Feldheim and Yinon Spinka (1) The Hebrew University of Jerusalem, Israel
(2) The University of British Columbia, Vancouver, Canada
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 Kotecký conjecture.
Keywords: Potts model, long-range order, phase transition, rigidity
Feldheim Ohad, Spinka Yinon: Long-range order in the 3-state antiferromagnetic Potts model in high dimensions. J. Eur. Math. Soc. 21 (2019), 1509-1570. doi: 10.4171/JEMS/866