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. PACS Number(s): 64.60.Ht, 05.70.Ln 43 Mod. Phys. Lett. B 2001.15:43-55. Downloaded from www.worldscientific.com by UNIVERSITY OF MELBOURNE on 09/17/13. For personal use only.

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 .…”