Critical Behaviour of the Gaussian Model on Sierpinski Carpets

Abstract

The Gaussian model on Sierpinski carpets with two types of nearestneighbour interactions K and Kw and twocorresponding types of the Gaussian distribution constants b andbw is constructed by generalizing that on a translationallyinvariant square lattice. The critical behaviours are studied by therenormalization-group approach and spin rescaling method. They are foundto be quite different from that on a translationally invariant square lattice.There are two critical points at (K* = b,Kw* = 0) and (K* = 0,Kw* = bw), and the correlation length critical exponents are calculated.