Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

Jeśus Salas; Alan D. Sokal

doi:10.1007/BF02199113

Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

Jeśus Salas, Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	551-579
Number of pages	29
Journal	Journal of Statistical Physics
Volume	86
Issue number	3-4
DOIs	https://doi.org/10.1007/BF02199113
State	Published - Feb 1997

Keywords

Antiferromagnetic Potts models
Dobrushin uniqueness theorem
Phase transition

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02199113

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abstract = "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 Kagom{\'e} lattice (q≥6). The proofs are based on the Dobrushin uniqueness theorem.",

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AU - Sokal, Alan D.

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N2 - 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.

AB - 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.

KW - Antiferromagnetic Potts models

KW - Dobrushin uniqueness theorem

KW - Phase transition

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JF - Journal of Statistical Physics

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ER -

Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

Abstract

Keywords

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