Comparison between the nearest and the next-nearest neighbor site-spin interactions in the Ising model

A comparison between the nearest and the next-nearest neighbor site-spin interactions in the Ising model of various dimensions is presented. First, by the aid of the Green's function method the exact algebraic equations of the site-spin for the 1d Ising chain, the 2d square and the 3d simple cubic Ising lattices, are established, respectively. Then, according to the recursion principle with respect to these equations of the site-spins the expressions of the nearest and the next-nearest neighbor site-spin interactions of variously dimensional Ising models are obtained. The comparison between the nearest and the next-nearest neighbor site-spin interactions displays that on nearing the transition temperature K, the distinction between these two kinds of interactions is obviously increasing. It shows that the short range ordering plays an important role in the critical behavior of the Ising system. In addition, the abnormal and non-monotonic dependencies of these two near-neighbor correlative interactions upon the magnetization are revealed in the 3d situation. (C) 2002 Elsevier Science Ltd. All rights reserved.