Ordered phase and phase transitions in the three-dimensional generalized six-state clock model

TL;DR

This paper investigates phase transitions and ordered phases in a 3D six-state clock model, revealing an intermediate incompletely ordered phase and confirming the nature of phase transitions through Monte Carlo and non-equilibrium methods.

Contribution

It introduces a detailed analysis of the phase diagram of the 3D six-state clock model, identifying an intermediate phase and characterizing phase transition types and critical exponents.

Findings

Existence of an incompletely ordered phase (IOP1) at intermediate temperatures.

High temperature transition aligns with 3D-XY universality class.

Low temperature transition is of first-order.

Abstract

We study the three-dimensional generalized six-state clock model at values of the energy parameters, at which the system is considered to have the same behavior as the stacked triangular antiferromagnetic Ising model and the three-state antiferromagnetic Potts model. First, we investigate ordered phases by using the Monte Carlo twist method (MCTM). We confirmed the existence of an incompletely ordered phase (IOP1) at intermediate temperature, besides the completely ordered phase (COP) at low-temperature. In this intermediate phase, two neighboring states of the six-state model mix, while one of them is selected in the low temperature phase. We examine the fluctuation the mixing rate of the two states in IOP1 and clarify that the mixing rate is very stable around 1:1. The high temperature phase transition is investigated by using non-equilibrium relaxation method (NERM). We estimate the critical exponents beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY universality class. The low temperature phase transition is found to be of first-order by using MCTM and the finite-size-scaling analysis.