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arXiv 2004.14662cond-mat.stat-mech
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正方形和蜂窝形Ising晶格的三自旋关联函数关系

Exact three spin correlation function relations for the square and the honeycomb Ising lattices

Tuncer Kaya

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18 pages
发表信息：
Chinese Journal of Physics (2020)
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摘要：

在这项工作中，序参数和两个网站的相关函数表示适当使用抽取变换过程中存在的外场，使它们的应用导致一些有意义的物理结果。事实上，它们的应用产生或再现了一些相关的和重要的结果，这些结果在以前的研究中被包括在繁琐的数学中，如果不是以一种不可能理解的形式。平均磁化强度或序参量$<\!\!σ\!\!> $表示为$<\!\!σ_{0,i}\!\!>= <\!\!\tanh[ κ(σ_{1,i}+σ_{2,i}+\dots +σ_{z,i})+H]\!\!> $。这里，$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$是中心自旋周围的最近邻自旋。$H$是归一化的外部磁场。我们表明，这种关系的应用程序的1D伊辛模型很容易再现以前获得的精确结果在没有外部场。进一步，解析地得到了正方形和蜂窝形晶格的三位关联函数，其形式为$<\!\!σ_{1}σ_{2}σ_{3}\!\!>$。我们发现三点相关函数等于$f(κ)\!\!<\!\!σ\!\!>$。这里$f(κ)$取决于晶格类型，并且是耦合常数的解析函数。这一结果表明，这些晶格的三格点关联函数的临界性质与相应的序参数$<\!\!σ\!\!>$相同。这意味着平均磁化强度作为序参量的唯一性是有问题的。...

英文摘要：

In this work, the order parameter and the two-site correlation functions are expressed properly using the decimation transformation process in the presence of an external field so that their applications lead to some significant physical results. Indeed, their applications produce or reproduce some relevant and important results which were included in cumbersome mathematics in the previous studies, if not in a form impossible to understand. The average magnetization or the order parameter $<\!\!σ\!\!> $ is expressed as $<\!\!σ_{0,i}\!\!>= <\!\!\tanh[ κ(σ_{1,i}+σ_{2,i}+\dots +σ_{z,i})+H]\!\!> $. Here, $κ$ is the coupling strength, $z$ 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. $H$ is the normalized external magnetic field. We show that the application of this relation to the 1D Ising model reproduces readily the previously obtained exact results in the absence of an external field. Furthermore, the three-site correlation functions of square and honeycomb lattices of the form $<\!\!σ_{1}σ_{2}σ_{3}\!\!>$ are analytically obtained. One finds that the three-site correlation functions are equal to $f(κ)\!\!<\!\!σ\!\!>$. Here $f(κ)$ depends on the lattice types and is an analytic function of coupling constant. This result indicates that the critical properties of three-site correlation functions of those lattices are the same as the corresponding order parameters $<\!\!σ\!\!>$ of those lattices. This will mean that the uniqueness of the average magnetization as an order parameter is questionable. ...

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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