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Physical review. B, Condensed matter

Monte Carlo simulation of the antiferromagnetic four-state Potts model on simple cubic and body-centered-cubic lattices

Mitsuhiro Itakura

Published Sep 1, 1999• 12 citations
Publisher

Abstract

The phase transition of four-state antiferromagnetic Potts model on simple cubic and body-centered-cubic lattice is studied by cluster Monte Carlo simulations of finite systems up to ${96}^{3}$ lattice sizes. The result indicates that the size ${96}^{3}$ is still sufficient to extract asymptotic behavior. However, if one assumes that both models are well described by the usual Ginzburg-Landau Hamiltonian, the result is consistent with the prediction of the field-theoretical analysis that the phase transition is first-order one.

DOI
10.1103/physrevb.60.6558

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Using the Monte Carlo method we investigate the phase transitions and thermodynamic properties of magnetic structures with noncollinear directions of magnetic moments corresponded to antiferromagnetic q=4 Potts model on a face-centered cubic lattice. Monte Carlo simulations are performed on lattices with linear sizes L=20÷44. Thermodynamic parameters: the order parameter mAF, susceptibility χ, internal energy U, and specific heat C are evaluated for all studied systems. By employing the fourth order Binder cumulant method, a first order transition is shown to be occurred in the model.
We have studied phase transitions and thermodynamic properties of the antiferromagnetic Potts model with number of spin states q = 3 on a body-centered cubic lattice by the Monte Carlo method. Investigations have been performed with account for exchange interactions J1 and J2 between the first and second nearest neighbors. The phase transition order has been analyzed using the histogram method. It is found that in this model with J2 = 0, a second-order phase transition is observed. It is concluded that the inclusion of the interaction between the second nearest neighbors changes the type of the phase transition.
Monte Carlo simulations and renormalization-group ideas are used to analyze the behavior of the antiferromagnetic Potts model and the Ashkin-Teller model in three dimensions. A variety of continuous transitions, observed in the Monte Carlo data on the antiferromagnetic Potts model for simple cubic and body-centered-cubic lattices, are found to be consistent with $\ensuremath{\epsilon}$-expansion analyses of these models. A glassy "plastic crystal" phase is observed, along with the analog of the glass transition in the four-state antiferromagnetic Potts model. An $\ensuremath{\epsilon}$-expansion analysis of the Ashkin-Teller model is found to yield results consistent with those obtained by Ditzian et al. using series analysis and Monte Carlo simulations.
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.