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Journal of Physics A Mathematical and General

Three-state square lattice Potts antiferromagnet

M. P. Nightingale, Michael Schick C

Published Jan 1, 1982• 55 citations
Publisher

Abstract

The three state antiferromagnetic Potts model on a square lattice is investigated via phenomenological renormalisation group methods. In contrast to previous calculations, the results indicate that there exists neither an ordered phase nor a massless phase with algebraic decay of correlations. The sole critical point is at zero temperature, where an essential singularity is found.

DOI
10.1088/0305-4470/15/1/008

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The three state antiferromagnetic Potts model on a square lattice is investigated via phenomenological renormalisation group methods. In contrast to previous calculations, the results indicate that there exists neither an ordered phase nor a massless phase with algebraic decay of correlations. The sole critical point is at zero temperature, where an essential singularity is found.
We study a square-lattice three-state Potts antiferromagnet with a staggered polarization field at finite temperature. Numerically treating the transfer matrices, we determine two phase boundaries separating the model-parameter space into three parts. We confirm that one of them belongs to the ferromagnetic three-state Potts criticality, which is in accord with a recent prediction, and another to the Ising-type; these are both corresponding to the massless renormalization-group flows stemming from the Gaussian fixed points. We also discuss a field theory to describe the latter Ising transition.