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

TL;DR

This paper derives a scaling law for $Z_n$ models in 3D, confirms it with Monte Carlo data on the three-state antiferromagnetic Potts model, and supports a single massive ordered phase in the Renormalization-Group framework.

Contribution

It introduces a new scaling law for the $Z_n$ order parameter in three-dimensional models and validates it against numerical simulations.

Findings

The scaling law is consistent with Monte Carlo results.

Supports the existence of a single massive ordered phase.

Numerical observations of intermediate symmetry are explained by the theory.

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.