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arXiv · 1405.1179

Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

S. Wang·Z. Y. Xie·J. Chen·B. Normand·T. Xiang
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Abstract

We investigate the 2- and 3-state ferromagnetic Potts models on the simple cubic lattice using the tensor renormalization group method with higher-order singular value decomposition (HOTRG). HOTRG works in the thermodynamic limit, where we use the $Z_q$ 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 $T_c = 4.51152469(1)$. 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 the first-order nature of the phase transition and the HOTRG transition temperature benchmarks the most recent Monte Carlo result.

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S. Wang, Z. Y. Xie, J. Chen, B. Normand, T. Xiang. 2014-05-06. Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice. https://doi.org/10.1088/0256-307x%2F31%2F7%2F070503

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