Non-equilibrium Critical Dynamics of Ferromagnets with Long Range Correlated Defects

The simultaneous effect of non-equilibrium initial states and correlation between defects of the structure on the evolution of anisotropic disordered systems at the critical point was analyzed. The field theory description of the non-equilibrium critical behavior of three-dimensional disordered systems with the long-range correlated defects was given and the dynamical critical exponent of the short-time evolution was calculated in the two-loop approximation without the use of the E-expansion. The values of the dynamical critical exponent obtained by using various methods for summing asymptotic series were compared with the results of the computer simulation of the non-equilibrium critical behavior of the three-dimensional disordered Ising model in the short-time regime. The renormalization group analysis in [1] shows that if the initial state of a ferromagnetic system is characterized by a sufficiently high degree of the chaotization of spin variables with the relative magnetization far from the saturation state (m(0) << 1), the process of the relaxation of the system from a given initial non-equilibrium state at the critical point at macroscopically small times is accompanied by an anomalous increase in magnetization with time according to a power law with the exponent characterized by a independent dynamical critical exponent theta': m(t) similar to t(theta)'. (1) Janssen et al. [1] predicted a two-time dependence for the response function x(t, t(w)) and the correlation function C(t, t(w)) chi(t, t(w)) similar to (t/t(w))(theta), C(t, t(w)) (t/t(w))(theta-1) (2) and obtained the scaling relation theta' = theta + (2 - z - eta)/z between the exponents theta and theta'. In this work we study the effect of correlation between defects on the non-equilibrium critical behavior. The effect of extended defects such as dislocations or plane structural defects appearing at the grain boundary can be considered within the same framework. It can be expected that long-range correlation in the spatial distribution of defects can modify the critical properties of disordered systems. To describe the effect of complex extended defects on the critical behavior of system we investigate the Weinrib-Halperin model with the long-range isotropic correlation between defects when the pair correlation function g(x - y) decreases with an increase in the distance according to the power law: g(x - y) similar to vertical bar x - y vertical bar(-a) (3) where a is the correlation parameter of structural defects. In the presence of extended defects (randomly oriented dislocations or planes), its critical behavior can also be described within the framework of the Weinrib-Halperin model at the correlation parameter a = d - 1 or d - 2, respectively, where d is the dimension of the system.