Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

We investigate the 2- and 3-state ferromagnetic Ports models on the simple cubic lattice using the tensor renorrealization group method with higher-order singular value decomposition （FIOTRG）. HOTRG works in the thermodynamic limit, where we use the Zq symmetry of the model, combined with a new meas...

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Published inChinese physics letters Vol. 31; no. 7; pp. 41 - 45
Main Author 王顺 谢志远 陈靖 Bruce Normand 向涛
Format Journal Article
LanguageEnglish
Published 01.07.2014
Subjects
Accuracy
Benchmarks
Cubic lattice
Ferromagnetism
Mathematical analysis
Phase transformations
Thermodynamics
Transition temperature
三态模型
奇异值分解
对称模型
热力学极限
相变
立方晶格
蒙特卡洛
铁磁
Online AccessGet full text
ISSN0256-307X
1741-3540
DOI10.1088/0256-307x/31/7/070503

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Summary:We investigate the 2- and 3-state ferromagnetic Ports models on the simple cubic lattice using the tensor renorrealization group method with higher-order singular value decomposition （FIOTRG）. HOTRG works in the thermodynamic limit, where we use the Zq symmetry of the model, combined with a new measure for detecting the transition, to improve the accuracy of the critical point for the 2-state model by two orders of magnitude, obtaining Tc = 4.51152469（1）. The 3-state model is far more complex, and we improve the overall understanding of this case by calculating its thermodynamic quantities with high accuracy. Our results verify that the first-order nature of the phase transition and the HOTRG transition temperature benchmarks the most recent Monte Carlo result.
Bibliography:11-1959/O4
We investigate the 2- and 3-state ferromagnetic Ports models on the simple cubic lattice using the tensor renorrealization group method with higher-order singular value decomposition （FIOTRG）. HOTRG works in the thermodynamic limit, where we use the Zq symmetry of the model, combined with a new measure for detecting the transition, to improve the accuracy of the critical point for the 2-state model by two orders of magnitude, obtaining Tc = 4.51152469（1）. The 3-state model is far more complex, and we improve the overall understanding of this case by calculating its thermodynamic quantities with high accuracy. Our results verify that the first-order nature of the phase transition and the HOTRG transition temperature benchmarks the most recent Monte Carlo result.
WANG Shun, XIE Zhi-Yuan, CHEN Jing , Bruce Normand, XIANG Tao（ 1 Institute of Physics, Chinese Academy of Sciences, Beijing 100190 ;2Department of Physics, Renmin University of China, Beijing 100872）
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ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307x/31/7/070503