摘要
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.
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.
基金
Supported by the National Natural Science Foundation of China under Grant Nos 10934008, 10874215, and 11174365, and the National Basic Research Program of China under Grant Nos 2012CB921704 and 2011CB309703.
