Critical Behaviour of the Gaussian Model on Sierpinski Carpets

The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and K_w and two corresponding types of the Gaussian. distribution constants b and b_w is constructed by generalizing that on translationally invariant square lattice. The critical behaviours are studied by the renormalization-group approach and spin rescaling method. They are found to be quite different from that on translationally invariant square lattice. There are two critical points at (K^* = b,K^*_w = 0) and (K^* = 0,K^*_w = b_w), and the correlation length critical exponents are calculated.