论文标题
方格伊辛模型的磁敏感性
Magnetic susceptibility of the square lattice Ising model
论文作者
论文摘要
在这项工作中，使用最近获得的平均磁化相互关系研究了方格晶格模型的敏感性，该磁化相互关系由$ \langleσ_{0，i} \ rangle = \ langle \ langle \ langle \ tanh [k（σ_（σ_）） $。在这里，$ z $是最近的邻居的数量，$σ_{0，i} $表示$ i^{th} $网站的中心旋转，而$σ_{l，i} $，$ l = 1,2，\ dots，z $是中心周围的最接近邻居，$ k = j/（$ k = $ k_ {b} $是玻尔兹曼的常数，$ t $是系统的温度。在我们的研究中，不可避免地，我们必须对本文获得的关系中出现的三个站点相关函数做出猜想。三个自旋相关函数的猜想形式由关系给出，$ \langleσ_{1}σ_{2}σ_{3} \ rangle = a（k，k，k，h）\langleσ\ rangle+rangle+[1- a（k，k，k，k，k，h）]在这里，$β$表示平均磁化的关键指数，$ a（k，h）$是一个函数，其行为将以任意常数为临界点围绕临界点进行描述。为了阐明本文中使用的方法的相关性，我们首先计算了1D链的敏感性，并且所获得的敏感性表达被视为等同于常规方法的敏感性结果。方格晶格iSing模型的磁性关键指数$γ$以$γ= 1.72 $的价格，对于$ t \！> \！> \！t_ {c} $，$γ= 0.91 $ for $ t \！<\！<\！<\！t_ {c} $。
In this work, the susceptibility of the square lattice Ising model is investigated using the recently obtained average magnetization interrelation, which is given by $\langleσ_{0, i}\rangle= \langle\tanh[K(σ_{1,i}+σ_{2,i}+\dots +σ_{z,i})+H]\rangle $. Here, $z$ 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, $K=J/(k_{B}T)$, where $J$ is the nearest neighbor coupling constant, $k_{B}$ is the Boltzmann's constant and $T$ is the temperature of the system. 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, $\langleσ_{1}σ_{2}σ_{3}\rangle=a(K,H)\langleσ\rangle+[1-a(K,H)]\langleσ\rangle^{(1+β^{-1})}$. Here $β$ denotes the critical exponent for the average magnetization and $a(K,H)$ is a function whose behavior will be described around the critical point with an arbitrary constant. To elucidate the relevance of the method used in this paper, we have first calculated the susceptibility of the 1D chain as an example, and the obtained susceptibility expression is seen as equivalent to the result of the susceptibility of the conventional method. The magnetic critical exponent $γ$ of the square lattice Ising model is obtained as $γ=1.72$ for $T\!>\!T_{c}$, and $γ=0.91$ for $T\!<\!T_{c}$.
