Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model

Abstract

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.

Critical behavior of a three-dimensional random-bond Ising model using finite-time scaling with extensive Monte Carlo renormalization-group method

“…So far, the static critical exponents obtained from RG analysis, ͓7͔ Monte Carlo ͑MC͒ simulations ͓10,11,16,18,19͔, and experiments ͓6͔ agree in general quite well. However, ␥ = 1.306 from a nonperturbative approach ͓20͔ and ␥ = 1.305͑5͒ from a high-temperature series expansion ͓8͔ are slightly smaller than ␥ = 1.400͑30͒ ͓6͔, ␥ = 1.330͑17͒ ͓7͔, ␥ = 1.342͑10͒ ͓10͔, ␥ = 1.341͑4͒ ͓16͔, ␥ = 1.342͑7͒ ͓18͔, and also ␥ = 1.34͑1͒ of the bond-diluted Ising model ͓11͔.…”

Monte Carlo renormalization group of dilute 3D Ising dynamics

“…A similar calculation performed in the three-loop approximation for diluted Ising system [26] with the use of different methods of summation gave the value z = 2.1792 (13). The comparison of these FTM results with our present MC results and results in [18,24] shows that they are in good agreement for weakly diluted systems with p = 0.95 and 0.8 and with experimental value of z = 2.18(10) obtained in [27] under investigations of the dynamic critical behavior of weakly diluted Ising-like magnet F e p Zn 1−p F 2 with p = 0.9. The simulation results give a much higher values of the dynamic exponent z for spin concentrations p = 0.6 and 0.5.…”

“…However, it remains unclear whether the asymptotic values of critical exponents are independent of the rate of dilution of the system, how the crossover effects change these values, and whether two or more regimes of the critical behavior exist for weakly and strongly disordered systems. These questions are the subjects of heated discussions [2,15] and extensive Monte Carlo simulations for site-diluted [16][17][18] and bond-diluted [19,20] three-dimensional Ising models.…”

Монте-Карло-Исследование Влияния Начальных Состояний И Дефектов Структуры На Неравновесное Критическое Поведение Трехмерной Модели Изинга

“…Ренормгрупповые [15,16], численные [17][18][19][20] и экспе-риментальные [21] методы исследования критической динамики структурно неупорядоченных систем позво-лили к настоящему времени однозначно установить, что присутствие в системах как некоррелированных дефектов структуры, так и дефектов с эффектами даль-нодействующей корреляции приводит к новым типам критического поведения и заметному усилению эффек-тов критического замедления по сравнению с " чистыми" системами. В связи с этим особенности неравновесно-го поведения, такие как эффекты старения, несомнен-но должны найти более яркое проявление в струк-турно неупорядоченных системах с новыми универ-сальными значениями флуктуационно-диссипативного отношения.…”

“…Когда выполняется следующее их соответ-ствие t w < t ≪ t m , реализуемое для случая эволюции из высокотемпературного начального состояния с m 0 = 0, зависимости (18) для C(t, t w , t m ) и χ(t, t w , t m ) переходят в соотношения, соответствующие этому случаю [6,24]. Случай эволюции из высокотемпературного начального состояния с m 0 = 0 был детально исследован нами мето-дами Монте-Карло для чистой и структурной неупорядо-ченной трехмерной модели Изинга в работах [23,24,32].…”