论文标题
正方形和蜂窝晶格的精确三个自旋相关功能关系
Exact three spin correlation function relations for the square and the honeycomb Ising lattices
论文作者
论文摘要
在这项工作中，在存在外场的情况下，使用分解转换过程可以正确表达顺序参数和两端相关函数，以便它们的应用导致一些重要的物理结果。实际上，它们的应用产生或复制了一些相关和重要的结果，这些结果包括在先前的研究中繁琐的数学中，即使不是无法理解的形式。平均磁化或顺序参数$ <\！\！σ\！\！> $表示为$ <\！\！σ_{0，i} \！\！> = = = <\！\！\ tanh [κ（σ_{1，i}+σ_{2，i}+\ dots+σ_{z，i}，i}）+h] \！\！\！> $。在这里，$κ$是耦合强度，$ z $是最近的邻居数量。 $σ_{0，i} $表示$ i^{th} $站点的中心旋转，而$σ_{l，i} $，$ l = 1,2，\ dots，z $是中央旋转周围最近的邻居旋转。 $ H $是归一化的外部磁场。我们表明，这种关系与1D ISING模型的应用很容易在没有外部场的情况下重现先前获得的确切结果。此外，形式$ <\！\！σ_{1}σ_{2}σ_{3} \！\！> $的平方和蜂窝晶格的三个位点相关函数是分析获得的。人们发现，三个站点相关函数等于$ f（κ）\！\！<\！\！σ\！\！> $。这里$ f（κ）$取决于晶格类型，是耦合常数的分析函数。该结果表明这些晶格的三个位点相关函数的临界属性与相应的顺序参数$ <\！\！σ\！\！> $相同。这将意味着平均磁化作为顺序参数的唯一性是值得怀疑的。 ...
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. ...
