The magnetic structures of the ground state, phase transitions, and the thermodynamic properties of a two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a kagome lattice are studied using the Wang-Landau algorithm of the Monte Carlo method, taking into account the interactions of the nearest and the next-nearest neighbors. The studies were carried out for the value of the interaction of the next-nearest neighbors in the range 0 ≤ r ≤ 1.0. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbor leads to a violation of the magnetic ordering. A phase diagram of the dependence of the critical temperature on the value of the interaction of the next-nearest neighbor is constructed. The analysis of the character of phase transitions is carried out. It was found that in the ranges 0 ≤ r ≤ 0.5 and 0.5 ≤ r ≤ 1.0, a first-order phase transition is observed, and for r = 0.5, frustrations are observed in the system.

中文翻译：

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在 Kagome 晶格上自旋态数 q=4 的 Potts 模型的相图

 使用蒙特卡罗方法的 Wang-Landau 算法研究了 kagome 晶格上自旋态数q = 4的二维铁磁 Potts 模型的基态磁性结构、相变和热力学性质，考虑最近邻和次近邻的相互作用。研究是针对 0 ≤ r范围内的下一个最近邻的相互作用值进行的  ≤ 1.0。结果表明，考虑到下一个最近邻的反铁磁相互作用会导致违反磁序。构建了临界温度对次近邻相互作用值的依赖性的相图。对相变的特征进行了分析。发现在 0 ≤ r  ≤ 0.5 和 0.5 ≤  r  ≤ 1.0的范围内 ，观察到一阶相变，并且对于r  = 0.5，在系统中观察到挫折。