Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

TL;DR

This paper applies the HOTRG method to study phase transitions in 2- and 3-state ferromagnetic Potts models on a cubic lattice, achieving highly accurate critical points and confirming the nature of the phase transition.

Contribution

It introduces an improved HOTRG approach with symmetry considerations to precisely determine critical points and phase transition types in Potts models.

Findings

Achieved a critical temperature of 4.51152469(1) for the 2-state model.

Confirmed the first-order phase transition in the 3-state model.

Provided high-accuracy thermodynamic quantities for the 3-state model.

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.