Magnetization Distribution on Fractals and Percolation Lattices

Details Magnetization Distribution on Fractals and Percolation Lattices Magnetization Distribution on Fractals and Percolation Lattices

1996-03-08

arxiv.org/abs/cond-mat/9603065v1

Physics

Condensed Matter

Jour. Phys. I (France)

Scientific paper

10.1051/jp1:1996237

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 threshold 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 $T_g \simeq A_g/n$. An estimation of the ratio $T^{*}/T_g$ yields an estimation of the order of ramification of bidimensional percolation clusters at the threshold ($C = 2.3 \pm 0.2$).

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