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arXiv 2103.08470cond-mat.stat-mech
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正方形和蜂窝状伊辛晶格的相关交替解析平均磁化强度计算方法

Relevant alternative analytic average magnetization calculation method for the square and the honeycomb Ising lattices

Tuncer Kaya

备注：
12 pages, 2 figures
发表信息：
Chinese Journal of Physics, 77 (2022) 747-752
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摘要：

本文基于最近得到的磁化强度关系式$<σ_{0,i}>= <\!\!\tanh[ κ(σ_{1,i}+σ_{2,i}+\dots +σ_{z,i})+H]\!\!> $，得到了正方形和蜂窝晶格的序参量或平均磁化强度表达式。其中，$κ$是耦合强度，$z$是最近邻数。$σ_{0,i}$表示$i^{th}$位点处的中心自旋，而$σ_{l,i}$、$l=1,2,\dots,z$是中心自旋周围的最近邻自旋。在我们的研究中，不可避免地要对本文所得到的关系式中出现的三位关联函数作出一个猜想。三自旋相关函数的表达式由关系式$<\!\!σ_{1}σ_{2}σ_{3}\!\!>=a<σ>+(1-a)<σ>^{(1+β^{-1})}$给出，其中$β$表示平均磁化强度的临界指数，$a$是小于1的正实数。这个猜想的相关性是基于基本的物理推理。此外，通过将本文所得到的关系式与以前得到的正方形和蜂窝格子的精确结果进行比较，对本文所得到的关系式进行了检验和研究。可以看出，所得到的平均磁化强度关系与以前得到的精确结果的一致性是空前完美的。

英文摘要：

In this work, the order parameter or average magnetization expressions are obtained for the square and the honeycomb lattices based on recently obtained magnetization relation, $<σ_{0,i}>= <\!\!\tanh[ κ(σ_{1,i}+σ_{2,i}+\dots +σ_{z,i})+H]\!\!> $. Where, $κ$ is the coupling strength and $z$ is the number of nearest neighbors. $σ_{0,i}$ denotes the central spin at the $i^{th}$ site while $σ_{l,i}$, $l=1,2,\dots,z$, are the nearest neighbor spins around the central spin. In our investigation, inevitably we have to make a conjecture about the three site correlation function appearing in the obtained relation of this paper. The conjectured form of the the three spin correlation function is given by the relation, $<\!\!σ_{1}σ_{2}σ_{3}\!\!>=a<σ>+(1-a)<σ>^{(1+β^{-1})}$, here $β$ denotes the critical exponent for the average magnetization and $a$ is positive real number less than one. The relevance of this conjecture is based on fundamental physical reasoning. In addition, it is tested and investigated by comparing the obtained relations of this paper with the previously obtained exact results for the square and honeycomb lattices. It is seen that the agreements of the obtained average magnetization relations with those of the previously obtained exact results are unprecedentedly perfect.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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