Abstract

A diagonally connected two-dimensional lattice is the objective of the research. The model draws interest because each of its spins has 6 connects as in a 3D lattice. On the other hand, the planarity of the model allows us to use a strict polynomial algorithm to find its partition function and other characteristics. The Kasteleyn-Fisher algorithm is employed to carry out a computer simulation which enables us to see how the heat capacity behaves with the increasing lattice dimensionality. Given a finite lattice dimensionality, it is impossible to draw a definite conclusion, yet there is every reason to believe that the heat capacity diverges logarithmically at the critical point.

中文翻译：

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下一个邻居加法引起的二维Ising模型关键参数变化

摘要

对角连接的二维晶格是研究的目标。该模型引起了人们的兴趣，因为其每个自旋都具有3D晶格中的6个连接。另一方面，模型的平面性允许我们使用严格的多项式算法来找到其分区函数和其他特征。使用Kasteleyn-Fisher算法进行计算机仿真，使我们能够观察热容量如何随晶格尺寸的增加而变化。给定有限的晶格尺寸，不可能得出确定的结论，但是有充分理由相信，在临界点处，热容会以对数形式出现分歧。