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Chin. Phys. B, 2018, Vol. 27(8): 080503    DOI: 10.1088/1674-1056/27/8/080503
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Phase transitions of the five-state clock model on the square lattice

Yong Chen(陈勇)1, Zhi-Yuan Xie(谢志远)2, Ji-Feng Yu(余继锋)1
1 Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410082, China;
2 Department of Physics, Renmin University of China, Beijing 100872, China

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.

Keywords:  five-state clock model      phase transition      tensor renormalization group      HOTRG  
Received:  23 April 2018      Revised:  12 May 2018      Published:  05 August 2018
PACS:  05.70.Fh (Phase transitions: general studies)  
  05.10.Cc (Renormalization group methods)  
  75.10.Hk (Classical spin models)  

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).

Corresponding Authors:  Ji-Feng Yu     E-mail:

Cite this article: 

Yong Chen(陈勇), Zhi-Yuan Xie(谢志远), Ji-Feng Yu(余继锋) Phase transitions of the five-state clock model on the square lattice 2018 Chin. Phys. B 27 080503

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