Gaussian Field Theories on General Networks and the Spectral Dimensions

Abstract

We study rigorously the spectral dimension of a Gaussian field theory on a general network defined through the critical behavior (the massless singularity). We emphasize the methods of analysis such as random walk expansions and renormalization group ideas that can be used for systems without translational invariance. We derive universality properties, and give a rigorous method of calculating the spectral dimension for a special class of fractal networks.