Phase transitions of the five-state clock model on the square lattice**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 531107040857), the Natural Science Foundation of Hunan Province, China (Grant No. 851204035), and the National Natural Science Foundation of China (Grant No. 11774420).

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 by the correlation function at three representative temperatures. By calculating the magnetic susceptibility, we obtained only the upper critical temperature as Tc2 = 0.9565(7). Investigating the fixed-point tensor, we precisely locate the transition temperatures at Tc1 = 0.9029(1) and Tc2 = 0.9520(1), consistent well with the Monte Carlo and the density matrix renormalization group results.