Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Articles dans des revues à comité de lecture

Monte-Carlo study of anisotropic scaling generated by disorder
Vasilyev O., Berche B., Dudka M., Holovatch Yu.
Phys.Rev. E 92 (2015) 042118 1-9
DOI : 10.1103/PhysRevE.92.042118
ArXiv : arxiv:1504.07588 [PDF]

We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $\xi_\parallel$ in the direction along defects, and a perpendicular correlation length $\xi_\perp$ in the direction perpendicular to the lines. Both $\xi_\parallel$ and $\xi_\perp$ diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents $\nu_\parallel$ and $\nu_\perp$ take different values. This property is specific for anisotropic scaling and the ratio $\nu_\parallel/\nu_\perp$ defines the anisotropy exponent $\theta$. Estimates of quantitative characteristics of the critical behaviour for such systems were only obtained up to now within the renormalization group approach. We report a study of the anisotropic scaling in this system via Monte Carlo simulation of the three-dimensional system with Ising spins and non-magnetic impurities arranged into randomly distributed parallel lines. Several independent estimates for the anisotropy exponent $\theta$ of the system are obtained, as well as an estimate of the susceptibility exponent $\gamma$. Our results corroborate the renormalization group predictions obtained earlier.



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