On the phase diagram of the discrete $Z_6$ spin models

TL;DR

This paper revises the phase diagram of the $Z_6$ spin models by identifying issues in previous diagrams, proposing modifications, and supporting these with numerical evidence using a new phase space parametrization.

Contribution

It introduces a corrected phase diagram for $Z_6$ spin models and a novel parametrization, supported by numerical analysis.

Findings

Previous phase diagram had deficiencies near the decoupling surface

Proposed modifications improve the phase diagram accuracy

Numerical results support the new conjectures

Abstract

We point out some problems with the previously-proposed phase diagram of the $Z_6$ spin models. Consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies these deficiencies. With the aid of a new parametrisation of the phase space, we study the models numerically, with results which support our conjectures.