Magnetization Distribution on Fractals and Percolation Lattices

نویسنده

  • R. Mélin
چکیده

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 ∗ ≃ 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 Tg ≃ Ag/n. An estimation of the ratio T /Tg yields an estimation of the order of ramification of bidimensional percolation clusters at the threshold (C = 2.3± 0.2).

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تاریخ انتشار 1996