Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

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.

6 pages, 5 figures, 2 tables

References in corpus (6)

• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Phase Transition Properties of 3D Potts Models
• Accurate exponents from approximate tensor renormalizations
• Normalized entropy density of the 3D 3-state Potts model

Cited by in corpus (19)

• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Higher order tensor renormalization group for relativistic fermion systems
• Bond-weighted Tensor Renormalization Group
• Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories
• Tensor renormalization group approach to (1+1)-dimensional Hubbard model
• Partial long-range order in antiferromagnetic Potts models
• Collective Monte Carlo updates through tensor network renormalization
• Efficient calculation of three-dimensional tensor networks
• Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking
• Complex entanglement entropy for complex conformal field theory
• All-mode Renormalization for Tensor Network with Stochastic Noise
• A Fuzzy Sphere Journey in Critical Phenomena
• Efficient optimization of variational tensor-network approach to three-dimensional statistical systems
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
• Essential difference between 2D and 3D from the perspective of real-space renormalization group
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice