J. Phys. I France 6 (1996) 793-806
Maghetization Distribution on Fractals and Percolation LatticesR. 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)
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 , 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 . An estimation of the ratio yields an estimation of the order of ramification of bidimensional percolation clusters at the threshold ( ).
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