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

Ohad N. Feldheim*, Yinon Spinka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We prove the existence of long-range order for the 3-state Potts antiferromagnet at low temperature on Zd 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.

Original languageAmerican English
Pages (from-to)1509-1570
Number of pages62
JournalJournal of the European Mathematical Society
Issue number5
StatePublished - 2019

Bibliographical note

Funding Information:
Research of O.F. was conducted at Tel-Aviv University and the IMA, and was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.

Funding Information:
Research of Y.S. was conducted at Tel-Aviv University and was supported by Israeli Science Foundation grant 1048/11, Marie Skłodowska-Curie IRG grant SPTRF, and the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.

Publisher Copyright:
© European Mathematical Society 2019.


  • Long-range order
  • Phase transition
  • Potts model
  • Rigidity


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