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Chinese Physics Letters

Investigation of the Potts Model on Triangular Lattices by the Second Renormalization of Tensor Network States

Wang Meng-Xiong, Cai Jian-Wei, Z. Y. Xie, Chen Qiao-Ni, Hui‐Hai Zhao, Wei Zhong-Chao

Published Jul 1, 2010• 8 citations
Publisher

Abstract

We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q = 3 antiferromagnetic Potts model, the critical temperature is found to be T c = 0.627163±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods.

DOI
10.1088/0256-307x/27/7/076402

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Investigation of the Potts Model on Triangular Lattices by the Second Renormalization of Tensor Network States

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We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q = 3 antiferromagnetic Potts model, the critical temperature is found to be T c = 0.627163±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods.
The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.
The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.
By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius ν.
Phase transitions in the two-dimensional ferromagnetic Potts model with the number of spin states q = 3 on a triangular lattice were studied using Monte-Carlo method. The systems of linear size L = 20–120 were considered. Using the method of the fourth-order Binder cumulants, it was demonstrated that the second order phase transition is observed in the two-dimensional ferromagnetic Potts model. The static critical exponents for the heat capacity α, susceptibility γ, magnetization β and correlation radius ν were calculated based on the finite-dimensional scaling theory.