Short-Time Critical Behavior of Systems with Random Impurities

Abstract

The theoretical renormalization-group approach is applied to the study of the short-time critical behavior of the Ginzburg-Landau model with long-range random impurities which have a power-like correlation r ÀðdÀqÞ . The system initially at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with a model A dynamics. The asymptotic scaling laws are studied in the frame of a double expansion in E ¼ 4 À d and d ¼ E þ q with d of the order of E. The initial slip exponent q 0 for the order parameter is calculated up to the first order in E ¼ 4 À d or in E 1=2 corresponding to different fixed points, respectively. For d < 4, the short-time behavior of the order parameter is investigated in one loop. Two different logarithmic and exponential-logarithmic corrections to short-time behaviors of both the autocorrelation and the order parameter are also solved in d ¼ 4 dimension. Crossover between the nonrandom behavior and quenched behavior is found for n ¼ 4 (where n is the spin dimensionality) in d ¼ 4 dimension.

Short-Time Critical Behavior of the Ginzburg–landau Model With Quenched Disorder

“…They coincide at n = 4, indicating a crossover between the non-random behavior and the quenched disorder behavior, in agreement with the SRI results of Ref. 5. The Ising systems with SRQD display the very distinguished exponential-logarithmic corrections to the scaling laws for τ < τ x in contrast to the usual logarithmic scaling behaviors.…”

“…Notably, the Ising case depends upon the interaction, but at σ = 2 − η sr cannot recover the SRI results. 5 In summary, the short-time critical behavior of the Ginzburg-Landau model with the LRI and the LRQD are studied by the theoretic RG approach. Asymptotic scaling laws are obtained.…”

“…Universal short-time scalings have been found in a range of different models. [1][2][3][4][5] In the short-time stage of a system quenched from a high temperature to the critical temperature T c , an interesting phenomenon is that the order-parameter has a power law increase m(t) ∼ m 0 t θ , and the full-response function behaves as G p (t, t ) ∼ (t/t ) θ for t → 0. For a short time after the quench, the scaling behaviors are governed by the initial slip exponents θ and θ .…”

Nonequilibrium critical relaxation in the presence of extended defects

“…In recent years, much attention has been attracted by the so-called short-time critical dynamics. 1,2,3,4,5,6,7,8,9 A thermodynamic system in a critical point is characterized by long-range correlations in equilibrium, so when such a system is quenched from a high temperature T 0 ≫ T c to the critical point T c , the growth of correlations governs the relaxation process. As shown in Ref.…”

Two-loop Feynman integrals for ϕ4 theory with long-range correlated disorder

“…As it is shown below, massive Feynman integrals in this case may have additional massless propagators. Effects of such long-range correlated disorder on the critical properties of φ 4 model were studied intensively including static critical behaviour [37][38][39][40][41] , critical dynamics near equilibrium 38,39,41,42 , short time critical dynamics [43][44][45] , critical ultrasound propagation 46 .…”