一种分形点阵上含两体和四体互作用Ising模型的严格解  

EXACT SOLUTION OF AN ISING MODEL WITH PAIR AND FOUR-SITE INTERACTIONS ON A FRACTAL LATTICE

作　　者：秦勇[1] 

机构地区：[1]北京师范大学物理系,北京新外大街100875

出　　处：《北京师范大学学报（自然科学版）》1993年第1期64-67,共4页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金;国家教委博士点基金

摘　　要：研究了被称为Diamond阶梯点阵的分形结构上的含两体和四体互作用的Ising模型。发现该系统可以等价于仅含两体互作用的系统。因此,四体互作用不影响系统的临界行为。得到了所考虑系统的临界行为的严格解及相图。特别是当四体互作用常数J_4<0时,存在一个相变截止值r_c=-2。当r<-2时,系统在所有温度均处于无序相。这里,r=J_4/|J_2|。An Ising model with two- and four-site couplings on the dia- mond hierarchical lattice as a kind of fractal lattice is considered. It is found that the system is equivalent to one with pure nearest-neighbor pair interac- tion on the same lattice, and the two systems have the same critical beha- vior. The exact equation of critical curve and phase diagram are obtained for the system. In particular, there is a cutoff value r_c=-2 as four-site coupling constant J_4<0. For r<-2 the system is in disordered phase at any temperature, where r=J_2/|J_2|.

关 键 词：分形 伊辛模型 相变 统计物理学 

分 类 号：O414.21[理学—理论物理]