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Journal of Physics A Mathematical and General

A first-order phase transition in the three-dimensional four-state antiferromagnetic Potts model

A Yamagata

Published Feb 7, 1993• 5 citations
Publisher

Abstract

Studies the four-state antiferromagnetic Potts model with next-nearest-neighbour ferromagnetic interactions on the simple cubic lattice by the Monte Carlo method. The ratio J 2 /J 1 of the strength of the next-nearest-neighbour interactions to that of the nearest-neighbour interactions is to be 10. The author analyses the finite-size effects of the energy, the specific heat, the fourth-order cumulant, the magnetization, the susceptibility and the effective transition temperatures. With the help of the finite-size scaling theory the author concludes that the transition of the model is assigned to be of first order.

DOI
10.1088/0305-4470/26/3/015

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Studies the four-state antiferromagnetic Potts model with next-nearest-neighbour ferromagnetic interactions on the simple cubic lattice by the Monte Carlo method. The ratio J 2 /J 1 of the strength of the next-nearest-neighbour interactions to that of the nearest-neighbour interactions is to be 10. The author analyses the finite-size effects of the energy, the specific heat, the fourth-order cumulant, the magnetization, the susceptibility and the effective transition temperatures. With the help of the finite-size scaling theory the author concludes that the transition of the model is assigned to be of first order.
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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.
We performed a Monte Carlo simulation on a four-dimensional hypercube for the three-state Potts model with ferromagnetic nearest-neighbours interactions and antiferromagnetic next-nearest-neighbours interactions. We find that on the ferromagnetic branch of the critical line the phase transition is always of first order. This result, which is in agreement with Landau and mean-field theories, precludes the possibility of defining a continuum limit of the model and confirms the difficulties met in the construction of a four-dimensional nontrivial scalar field theory.
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 investigate the phase transition of the three-state Potts model in an analytical approach—the generalized cumulant expansion with the effective mean field hypothesis. We find a first order phase transition in the three-dimensional three-state Potts model with ferromagnetic nearest neighbor coupling. For the model with antiferromagnetic next-to-nearest neighbor coupling, we find a first order transition when the relative strength of the -coupling is fixed to . The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.
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.