Monte Carlo study of anisotropic scaling generated by disorder
Résumé
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 to) in the direction along defects and a perpendicular correlation length xi(&BOTT OM;) in the direction perpendicular to the lines. Both xi(parallel to) and xi(perpendicular to) diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents nu(parallel to) and nu(perpendicular to) take different values. This property is specific for anisotropic scaling and the ratio nu(parallel to)/nu(perpendicular to) defines the anisotropy exponent theta. Until now, estimates of quantitative characteristics of the critical behavior for such systems have been obtained only 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 nonmagnetic 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.