HAL CCSD
Critical behavior of the Ising model on random fractals
Monceau, Pascal
Matière et Systèmes Complexes (MSC) ; Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
HPC resources of IDRIS and CINES allocation 2010052127 made by GENCI
International audience
ISSN: 1539-3755
EISSN: 1550-2376
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
American Physical Society
hal-00645891
https://u-paris.hal.science/hal-00645891
https://u-paris.hal.science/hal-00645891
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 84 (5), pp.051132. ⟨10.1103/PhysRevE.84.051132⟩
DOI: 10.1103/PhysRevE.84.051132
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.84.051132
en
Phase transitions
critical phenomena
Ising model
Potts model
disordered systems
random fractals
Monte-Carlo simulations
lack of self averaging
68.35.Rh, 05.45.Df, 75.10.Hk, 75.40.Mg.
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
info:eu-repo/semantics/article
Journal articles
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.
2011-11-28