Real-space renormalization-group study of the phase transition in a Gaussian model of fractals

Abstract

In this paper the phase transition of the Gaussian model on m-sheet fractals (mSG${)}_{\mathrm{l}}$ and (mDH${)}_{\mathrm{l}}$ is investigated by the real-space renormalization-group method, i.e., decimation following a spin rescaling. The latter is introduced to keep the parameter b constant. Fixed points of the renormalization-group transformation are found and discussed. Our results show the existence of different properties of phase transition between the Gaussian model and the Ising model on fractals. In addition, we find that the critical point k=b/4 in a regular Sierpinski gasket is identified, with result of k=b/d (d is the coordination number) in Euclidean space. This indicates that the critical point of the Gaussian model may be uniquely determined by the coordination number whether on homogeneous fractals or translationally invariant lattices.