Phase transitions in a three-dimensional Ising model with cluster weight studied by Monte Carlo simulations.
Phase transitions in a three-dimensional Ising model with cluster weight studied by Monte Carlo simulations.
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DOI：
10.1103/physreve.104.044132
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Ziyang Wang;Le Feng;Wanzhou Zhang;Cheng-Yun Ding
中科院分区：
文献类型：
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作者：
Ziyang Wang;Le Feng;Wanzhou Zhang;Cheng-Yun Ding
环模型是统计力学中的一个重要模型，在二维晶格中得到了广泛的研究。然而，在三维格中，特别是在配位数大于3的格中，直接模拟环路模型仍然很困难。本文通过在传统的Ising模型的配分函数中引入一个额外的聚类权重n，提出了一种聚类权重Ising模型。该模型在二维晶格上与环模型等效，但在三维晶格上，这些模型是否具有相同的通用性仍然不是很清楚。采用具有聚类更新和颜色分配的蒙特卡罗方法，得到了包含顺磁相和铁磁相的全局相图。两相之间的相变在1≤n<n_{cri}处为二阶，在n≥n_{cri}处为一阶，其中n_{cri}≈2。当一阶跃迁发生时，热指数y_{t}等于系统维数d。对于二阶跃迁，对y_{t}和磁指数y_{m}的数值估计表明，两种模型在三维晶格上的通用性是不同的。我们的结果有助于理解一些传统的统计力学模型。
The loop model is an important model of statistical mechanics and has been extensively studied in two-dimensional lattices. However, it is still difficult to simulate the loop model directly in three-dimensional lattices, especially in lattices with coordination numbers larger than 3. In this paper, a cluster weight Ising model is proposed by introducing an additional cluster weight n in the partition function of the traditional Ising model. This model is equivalent to the loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. By using a Monte Carlo method with cluster updates and color assignment, we obtain the global phase diagram containing the paramagnetic and ferromagnetic phases. The phase transition between the two phases is second order at 1≤n<n_{cri} and first order at n≥n_{cri}, where n_{cri}≈2. The thermal exponent y_{t} is equal to the system dimension d when the first-order transition occurs. For the second-order transitions, the numerical estimation of y_{t} and the magnetic exponent y_{m}, shows that the universalities of the two models on the three-dimensional lattice are different. Our results are helpful in the understanding of some traditional statistical mechanics models.