Abstract
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 language | American English |
|---|---|
| Pages (from-to) | 1509-1570 |
| Number of pages | 62 |
| Journal | Journal of the European Mathematical Society |
| Volume | 21 |
| Issue number | 5 |
| DOIs | |
| State | Published - 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.
Keywords
- Long-range order
- Phase transition
- Potts model
- Rigidity