Critical behavior of the Ising model on random fractals

Abstract : We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension d_{f}≃1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalisation flows are shown to be different from the ones calculated from ε expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.
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https://hal-univ-diderot.archives-ouvertes.fr/hal-00645891
Contributor : Pascal Monceau <>
Submitted on : Monday, November 28, 2011 - 5:43:20 PM
Last modification on : Monday, May 27, 2019 - 6:24:02 PM

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Pascal Monceau. Critical behavior of the Ising model on random fractals. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2011, 84 (5), pp.051132. ⟨10.1103/PhysRevE.84.051132⟩. ⟨hal-00645891⟩

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