Critical properties of the edge-cubic spin model on a square lattice

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 does well 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 ${\ensuremath{\nu}}_{h}=1.50(1)$ and ${\ensuremath{\nu}}_{l}=0.833(1)$. By using correlation ratio and size dependence of correlation function, we estimate the decay exponent for the high-$T$ transition as ${\ensuremath{\eta}}_{h}=0.260(1)$. For the low-$T$ transition, ${\ensuremath{\eta}}_{l}=0.267(1)$ is extracted from the finite size scaling of susceptibility. The universality class of the low-$T$ critical point is the same as the three-state Potts model.