SHORT-TIME CRITICAL BEHAVIOR OF THE GINZBURG–LANDAU MODEL WITH QUENCHED DISORDER

Abstract

The theoretic renormalization-group approach is applied to the study of short-time dynamics of the d-dimensional n-component spin systems with long-range interactions r-(d+σ) and quenched disorder which has long-range correlations r-(d-ρ). Asymptotic scaling laws are obtained in a frame of double expansions in ∊=2σ-d and ρ with ρ of the order ∊. The static exponents are obtained exactly to all the order. The initial slip exponents θ′ for the order parameter and θ for the response function, as well as the dynamic exponent z, are calculated upto the first order in ∊. In d=2σ, in contrast to the unique logarithmic decay in the long-time regime which does not depend on σ, ρ, n and the disorder, we find rich scaling structures including logarithmic and exponential-logarithmic scalings in the short-time regime. Non-universal critical scalings of Ising systems are also discussed for d=2σ.