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.
Bibliographical noteFunding 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.
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.
© European Mathematical Society 2019.
- Long-range order
- Phase transition
- Potts model