Critical properties of edge-cubic spin model on square lattice

TL;DR

This study investigates the phase transitions of the edge-cubic spin model on a square lattice, revealing two successive symmetry breakings and characterizing their critical properties through Monte Carlo simulations.

Contribution

It provides the first detailed analysis of the edge-cubic spin model's phase transitions, identifying two distinct critical points and their universality classes.

Findings

Two successive phase transitions at T_h=0.602 and T_l=0.5422.

High-T transition has correlation length exponent ν_h=1.50.

Low-T transition belongs to the 3-state Potts universality class.

Abstract

The edge-cubic spin model on square lattice is studied via Monte Carlo simulation with cluster algorithm. By cooling the system, we found two successive symmetry breakings, i.e., the breakdown of $O_h$ into the group of $C_{3h}$ which then freezes into ground state configuration. To characterize the existing phase transitions, we consider the magnetization and the population number as order parameters. We observe that the magnetization is good at probing the high temperature transition but fails in the analysis of the low temperature transition. In contrast the population number performs well in probing the low- and the high-$T$ transitions. We plot the temperature dependence of the moment and correlation ratios of the order parameters and obtain the high- and low-$T$ transitions at $T_h = 0.602(1)$ and $T_l=0.5422(2)$ respectively, with the corresponding exponents of correlation length $\nu_h=1.50(1)$ and $\nu_l=0.833(1)$. By using correlation ratio and size dependence of correlation function we estimate the decay exponent for the high-$T$ transition as $\eta_h=0.260(1)$. For the low-$T$ transition, $\eta_l = 0.267(1)$ is extracted from the finite size scaling of susceptibility. The universality class of the low-$T$ critical point is the same as the 3-state Potts model.