Monte Carlo study of anisotropic scaling generated by disorder

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 ξ_∥ in the direction along defects and a perpendicular correlation length ξ_⊥ in the direction perpendicular to the lines. Both ξ_∥ and ξ_⊥ diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents ν_∥ and ν_⊥ take different values. This property is specific for anisotropic scaling and the ratio ν_∥/ν_⊥ defines the anisotropy exponent θ. 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 θ of the system are obtained, as well as an estimate of the susceptibility exponent γ. Our results corroborate the renormalization group predictions obtained earlier.