Maghetization Distribution on Fractals and Percolation Lattices

R. Mélin

doi:doi:10.1051/jp1:1996237

Issue		J. Phys. I France Volume 6, Number 6, June 1996


Page(s)		793 - 806
DOI		https://doi.org/10.1051/jp1:1996237

DOI: 10.1051/jp1:1996237
J. Phys. I France 6 (1996) 793-806

Maghetization Distribution on Fractals and Percolation Lattices

R. Mélin

CRTBT-CNRS, BP 166X, 38042 Grenoble Cedex 9, France

(Received 29 December 1995, received in final form 4 March 1996, accepted 6 March 1996)

Abstract
We study the magnetization distribution of the Ising model on two regular fractals (a hierarchical lattice, the regular simplex) and percolation clusters at the percolation thresh-old in a two dimensional imbedding space. In all these cases, the only fixed point is T=0. In the case of the two regular fractals, we show that the magnetization distribution is non trivial below $T^{*}\simeq A^{*}/n$ , with n the number of iterations, and A^* related to the order of ramification. The cross-over temperature T^* is to be compared with the glass cross-over temperature $T_{\rm g}\simeq A_{\rm g}/n$ . An estimation of the ratio $T^{*}/T_{\rm g}$ yields an estimation of the order of ramification of bidimensional percolation clusters at the threshold ( $C=2.3\pm 0.2$ ).