Abstract

The Wang–Landau algorithm of the Monte Carlo method is used to study the magnetic structures of the ground state, phase transitions, and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with number q = 4 of spin states in a hexagonal lattice with the interactions of the nearest (J₁) and next-to-nearest (J₂) neighbors. The exchange interaction ratios in the range of 0.0 ≤ r = |J₂/J₁| ≤ 1.0 are studied. A phase diagram of the dependence of the critical temperature on the exchange interaction value of the next-to-nearest neighbors is constructed. The nature of phase transitions is analyzed. It is found that a first-order phase transition is observed in the range of 0.1 ≤ r ≤ 1.0, while there is no phase transition in the system and a strong degeneracy of the ground state is observed at r = 0.0.

中文翻译：

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六边形晶格中自旋态数为 q = 4 的反铁磁 Potts 模型的相图

摘要

使用蒙特卡洛方法的 Wang-Landau 算法研究六方晶格中自旋态数为q = 4 的二维反铁磁 Potts 模型的基态磁结构、相变和热力学性质最近 ( J ₁ ) 和次近 ( J ₂ ) 邻居的相互作用。0.0 ≤ r = |范围内的交换相互作用比 J ₂ / J ₁| ≤ 1.0 被研究。构建了临界温度对次近邻的交换相互作用值的依赖性的相图。分析了相变的性质。发现在 0.1 ≤ r ≤ 1.0范围内观察到一阶相变，而系统中没有相变，并且在r = 0.0处观察到基态的强简并。