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Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions

Masaki Oshikawa
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Abstract

Based on a Renormalization-Group picture of $Z_n$ symmetric models in three dimensions, we derive a scaling law for the $Z_n$ order parameter in the ordered phase. An existing Monte Carlo calculation on the three-state antiferromagnetic Potts model, which has the effective $Z_6$ symmetry, is shown to be consistent with the proposed scaling law. It strongly supports the Renormalization-Group picture that there is a single massive ordered phase, although an apparently rotationally symmetric region in the intermediate temperature was observed numerically.

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Masaki Oshikawa. 1999-07-26. Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions. https://doi.org/10.1103/physrevb.61.3430

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