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

Abstract

We prove that theq-state Potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) wheneverq>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay forq≥7), triangular lattice (q≥11), hexagonal lattice (q≥4), and Kagomé lattice (q≥6). The proofs are based on the Dobrushin uniqueness theorem.

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Salas, J., Sokal, A.D. Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem. J Stat Phys 86, 551–579 (1997). https://doi.org/10.1007/BF02199113

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  • DOI: https://doi.org/10.1007/BF02199113

Key Words

  • Dobrushin uniqueness theorem
  • antiferromagnetic Potts models
  • phase transition