X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质

Critical behavior of the Gaussian model on X fractal lattices

Using the real-space renormalization group transformation method, critical behavior of the Gaussian model on two-dimension and %d%-dimension (%d%>2) X fractal lattices is studied. The results show that, at the critical point, the nearest-neighbor interaction parameter can be expressed in the form %K+*=b q-i/q-i(q-i% is the coordination number of site %i, b q-i% is the Gaussian distribution constant of site %i%), which is the same as that of other fractal lattices, and that the critical exponent %v% is associated with the space dimension %d% (or the fractal dimension %d%-f). They are much different from those of the Ising model on X fractal lattices.