REAL-SPACE RENORMALIZATION-GROUP STUDY OF THE PHASE-TRANSITION IN A GAUSSIAN MODEL OF FRACTALS

In this paper the phase transition of the Gaussian model on m-sheet fr actals (mSG)(l) and (mDH)(l) is investigated by the real-space renorma lization-group method, i.e., decimation following a spin rescaling. Th e latter is introduced to keep the parameter b constant. Fixed points of the renormalization-group transformation are found and discussed. O ur results show the existence of different properties of phase transit ion between the Gaussian model and the Ising model on fractals. In add ition, we find that the critical point k = b/4 in a regular Sierpinsk i 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 num ber whether on homogeneous fractals or translationally invariant latti ces.