论文标题
ISING系统的配置均值减少传输矩阵方法
Configurational Mean-Field Reduced Transfer Matrix Method for Ising Systems
论文作者
论文摘要
引入了高采型近邻居系统的平均场方法，并展示了该方法的应用。这项工作的主要思想是将Kadanoff的平均景点方法与以前我们中的一个人提出的模型相结合。引入平均场近似值是在伊斯丁·哈密顿式中的中央旋转替换为特定自旋构型的平均值，即在每种配置中考虑到近似值的平均值。该近似值用于两种不同的平均场类型方法。第一个考虑因素是一种纯种场型处理，其中所有相邻的旋转都被假定的构型平均替换。第二个考虑通过还原传输矩阵方法引入。通过使用马鞍点近似，通过数值和分析评估系统的临界耦合值的估计。第一个和第二个考虑因素中关键值的分析估计分别为$ k_ {c} = \ frac {1} {z} $和$（z-2）k_ {c} e^{2k_ {c}} = 1 $。显然，这两个考虑因素与确切治疗的偏差有显着偏差。在这项工作中，我们得出的结论是，此处介绍的方法比自洽的均值场型模型更合适，因为此处介绍的方法并不认为从一开始就存在相变的存在。因此，引入的方法有可能使我们的研究非常有价值的平均场型图片用于相变处理。
A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff's mean-field approach with the model presented by one of us previously. The mean-field approximation is introduced with the replacement of the central spin in Ising Hamiltonian with an average value of particular spin configuration, i.e, the approximation is taken into account within each configuration. This approximation is used in two different mean-field-type approaches. The first consideration is a pure-mean-field-type treatment in which all the neighboring spins are replaced with the assumed configurational average. The second consideration is introduced by the reduced transfer matrix method. The estimations of critical coupling values of the systems are evaluated both numerically and also analytically by the using of saddle point approximation. The analytical estimation of critical values in the first and second considerations are $ K_{c}=\frac{1}{z} $ and $ (z-2) K_{c}e^{2K_{c}} =1 $ respectively. Obviously, both of the considerations have some significant deviation from the exact treatment. In this work, we conclude that the method introduced here is more appropriate physical picture than self-consistent mean-field-type models, because the method introduced here does not presume the presence of the phase transition from the outset. Consequently, the introduced approach potentially makes our research very valuable mean-field-type picture for phase transition treatment.
