The Gaussian Model on the Inhomogeneous Fractal Lattices

The decimation real-space renormalization group and spin-rescaling methods are applied to the study of phase transition of the Gaussian model on fractal lattices. It is found that the critical point equals /2 ( is the distribution constant of Gaussian model) on nonbranching Koch curves. For inhomogeneous fractal lattices, it is proposed that the is replaced with ( is the coordination number of the site ) and satisfies a certain relation . Under this supposition we find that the critical point of the Gaussian model on a branching Koch curve can be expressed uniquely as .