Mei Tao
Department of Journal, Central China Normal University, Wuhan 430079, China.
Entropy (Basel). 2018 Apr 12;20(4):277. doi: 10.3390/e20040277.
We employ the spinor analysis method to evaluate exact expressions of spin-spin correlation functions of the two-dimensional rectangular Ising model on a finite lattice, special process enables us to actually carry out the calculation process. We first present some exact expressions of correlation functions of the model with periodic-periodic boundary conditions on a finite lattice. The corresponding forms in the thermodynamic limit are presented, which show the short-range order. Then, we present the exact expression of the correlation function of the two farthest pair of spins in a column of the model with periodic-free boundary conditions on a finite lattice. Again, the corresponding form in the thermodynamic limit is discussed, from which the long-range order clearly emerges as the temperature decreases.
我们采用旋量分析方法来评估有限晶格上二维矩形伊辛模型的自旋-自旋关联函数的精确表达式，特殊的过程使我们能够实际进行计算过程。我们首先给出了有限晶格上具有周期-周期边界条件的模型的关联函数的一些精确表达式。给出了热力学极限下的相应形式，其显示出短程有序。然后，我们给出了有限晶格上具有周期-自由边界条件的模型中一列中最远的一对自旋的关联函数的精确表达式。再次讨论了热力学极限下的相应形式，从中可以清楚地看出，随着温度降低，长程有序出现。
