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Physical review. B, Condensed matter

Short-time critical behavior of anisotropic cubic systems

Yuan Chen

Published Jan 26, 2001• 9 citations
Publisher

Abstract

The renormalization group approach is applied to the study of the short-time critical behavior of the d-dimensional n-component spin systems with cubic anisotropy. First, the system is quenched from high temperature to the critical temperature and then relaxes to equilibrium within model A dynamics. The asymptotic scaling laws and the initial slip exponents ${\ensuremath{\theta}}^{\ensuremath{'}}$ and $\ensuremath{\theta}$ of the order parameter and the response function, respectively, are calculated to the second order in $\ensuremath{\epsilon}=4\ensuremath{-}d.$ Logarithmic corrections to short-time behaviors of both the autocorrelation and the order parameter are found in $d=4$ dimension.

DOI
10.1103/physrevb.63.092301

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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—(d—ρ. The system initially at a high temperature is firstly quenched to the critical temperature Tc 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 ϵ = 4 — d and δ = ϵ + ρ with δ of the order of ϵ. The initial slip exponent θ′ for the order parameter is calculated up to the first order in ϵ = 4 — d or in ϵ1/2 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 = 4 dimension. Crossover between the nonrandom behavior and quenched behavior is found for n = 4 (where n is the spin dimensionality) in d = 4 dimension.
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.
Short-time critical behavior of the random n -vector model is studied by the theoretic renormalization-group approach. Asymptotic scaling laws are studied in a frame of the expansion in =4- d for n ≠1 and for n =1 respectively. In d <4, the initial slip exponents θ' for the order parameter and θ for the response function are calculated up to the second order in =4- d for n ≠1 and for n =1 at the random fixed point respectively. Our results show that the random impurities exert a strong influence on the short-time dynamics for d <4 and n < n c .
Short-time critical behavior of the random n-vector model is studied by the theoretic renormalization-group approach.Asymptotic scaling laws are studied in a frame of the expansion in e = 4 - d for n ≠ 1 and for n = 1respectively.In d ＜ 4,the initial slip exponents θ′ for the order parameter and θ for the response function are calculated up to the second order in e ＝ 4 - d for n ≠ 1 and for n ＝ 1 at the random fixed point respectively.Our results show that the random impurities exert a strong influence on the short-time dynamics for d ＜ 4 and n ＜ nc.``
The theoretic renormalization group approach is applied to the study of short-time critical behavior of the Ginzburg–Landau model with weakly long-range interactions . The system initially at a high temperature is firstly quenched to the critical temperature and then released to an evolution with a model A dynamics. A double expansion in and with of order is employed, where is the spatial dimension. The asymptotic scaling laws and the initial slip exponents and for the order parameter and the response function respectively are calculated to the second order in for close to 2.