Exact solution of a Z(4) gauge Potts model on planar lattices

TL;DR

This paper presents an exact solution for a Z(4) gauge Potts model on planar lattices, revealing critical lines and surfaces, and establishing universality with a spin-3/2 Ising model.

Contribution

It provides the first exact solutions for the Z(4) gauge Potts model on square and triangular lattices, identifying critical behaviors and universality classes.

Findings

Two Ising-type critical lines on square lattices.

Critical surfaces and lines on triangular lattices with different behaviors.

Z(4) gauge Potts model shares universality class with spin-3/2 Ising model.

Abstract

The exact solution of a general Z(4) gauge Potts model with a single and double plaquette representation of the action is found on a subspace of gauge-coupling parameters on the square and triangular lattices. The two Ising-type critical lines of a second-order phase transition for the model on a square lattice are found. For the model on a triangular lattice the two critical surfaces of an Ising-type and two nontrivial lines of a second-order phase transition with different critical behavior than on the critical surfaces are found. It is shown that a two dimensional (2D) general Z(4) gauge Potts model with single and double plaquette representation of the action and a 2D spin-3/2 Ising model belong to the same universality class.