Abstract

In the present paper we analyzed a change in the density of states of a two-dimensional Ising model when a next-next-neighbor interaction is introduced. In other words, we examined two-dimensional lattices with diagonal connections. The same as in a three-dimensional model in this case each spin has 6 connections. Since the model is planar, we can calculate the free energy and other characteristics of the system using a polynomial algorithm. We performed computer simulations using the Kasteleyn–Fisher algorithm, which allowed us to study changes of critical values and the density of states when a long-range interaction is taken into account. From the obtained results it follows that the interactions of the type analyzed here result in quantitative changes of the system’s characteristics, but they did not change them qualitatively. In particular, we again obtained a logarithmic divergence of the heat capacity in the critical point.

中文翻译：

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引入邻域交互时二维Ising模型的状态密度变化

摘要

在本文中，我们分析了引入下一个邻域相互作用时二维伊辛模型的状态密度变化。换句话说，我们检查了具有对角线连接的二维晶格。与这种情况下的三维模型相同，每个自旋具有6个连接。由于模型是平面的，因此我们可以使用多项式算法来计算系统的自由能和其他特征。我们使用Kasteleyn-Fisher算法进行了计算机模拟，当考虑到远程相互作用时，该算法使我们能够研究临界值的变化和状态的密度。从获得的结果可以看出，此处分析的类型的交互作用导致系统特性的定量变化，但它们没有定性地变化。特别是，