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Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem (1997)
| Venue: | J. Stat. Phys |
| Citations: | 67 - 4 self |
BibTeX
@ARTICLE{Salas97absenceof,
author = {Jesús Salas and Alan D. Sokal},
title = {Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem},
journal = {J. Stat. Phys},
year = {1997}
}
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Abstract
Dedicated to the memory of R.L. Dobrushin We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q> 2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q ≥ 7), triangular lattice (q ≥ 11), hexagonal lattice (q ≥ 4), and Kagomé lattice (q ≥ 6). The proofs are based on the Dobrushin uniqueness theorem. Key Words: Dobrushin uniqueness theorem, antiferromagnetic Potts models, phase transition. 1
