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


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 languageEnglish
Pages (from-to)1509-1570
Number of pages62
JournalJournal of the European Mathematical Society
Issue number5
StatePublished - 2019
Externally publishedYes


FundersFunder number
Marie Skłodowska-Curie
National Science Foundation
Israel Academy of Sciences and Humanities
Israel Science Foundation1048/11


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


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