Phase transitions of the five-state clock model on the square lattice

TL;DR

This study uses tensor renormalization group methods to analyze phase transitions in the five-state clock model on a square lattice, identifying two critical temperatures and confirming results with multiple computational approaches.

Contribution

The paper applies tensor renormalization group techniques to precisely determine the phase transition temperatures of the five-state clock model, providing new insights into its critical behavior.

Findings

Identified two phase transition temperatures, Tc1 and Tc2.

Confirmed critical temperatures with tensor, Monte Carlo, and DMRG methods.

Observed temperature dependence of specific heat and correlation functions.

Abstract

Using the tensor renormalization group method based on the higher-order singular value decomposition,we have studied the phase transitions of the five-state clock model on the square lattice.The temperature dependence of the specific heat indicates the system has two phase transitions, as verified clearly in the correlation function. By investigating the magnetic susceptibility, we can only obtain the upper critical temperature as Tc2 = 0.9565(7). From the fixed-point tensor, we locate the transition temperatures at Tc1 = 0.9029(1) and Tc2 = 0.9520(1), consistent with the MC and the DMRG results.