Short-time critical behavior of the Ginzburg-Landau model with quenched disorder

摘要

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+sigma)) and quenched disorder which has long-range correlations r(-(d-rho)). Asymptotic scaling laws are obtained in a frame of double expansions in epsilon = 2 sigma - d and rho with rho of the order epsilon. The static exponents are obtained exactly to all the order. The initial slip exponents theta' for the order parameter and theta for the response function, as well as the dynamic exponent z, are calculated upto the first order in epsilon. In d = 2 sigma, in contrast to the unique logarithmic decay in the long-time regime which does not depend on sigma, rho, 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 = 2 sigma. [References: 29]