Monte Carlo study of anisotropic scaling generated by disorder

Abstract

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.

Critical behavior of the two-dimensional Ising model with long-range correlated disorder

“…[10,11,[37][38][39][40][41][42][43]. The numerical studies of systems with parallel linear [44] and planar defects [45,46] were also performed.…”

Phase transitions in the diluted 2D three-state Potts model on a square lattice

“…The computer technologies and computational study methods have developed to their prevalence over the theoretical and experimental methods in studying the unordered magnetic systems. This is due to the fact that real systems always have complicating factors, which impede use of theoretical and experimental procedures [1][2][3][4][5]. Many of the known theoretical arrangements within a theory & field renormalization & group method becomes inoperative if applied to systems with disorder (see reviews [4,5]).…”

Фазовые переходы в трехмерной слабо разбавленной модели Поттса с q=5

“…Вектор исследования фазовых переходов (ФП) и критических свойств магнитных систем под воздействием беспорядка, сместился в сторону применения вычислительных методов. Это обусловлено тем, что моделирование с использованием методов Монте-Карло (МК) позволяет изучать более реалистичные модели и учитывать усложняющие факторы, всегда присутствующие в реальных материалах [1][2][3][4][5]. Этому способствуют и серьезно возросшие вычислительные возможности современных компьютеров, и множество новейших и мощных алгоритмов, специально разработанных для использования в этой области.…”