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Communications in Theoretical Physics

Short-Time Dynamics of the Random n -Vector Model

Yuan Chen, Zhibing Li, Fang Hai, He Shun-Shan, Situ Shu-Ping

Published Nov 15, 2001• 1 citation
Publisher

Abstract

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 .

DOI
10.1088/0253-6102/36/5/611

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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 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.
Short-time critical dynamics of a random Ising model (model A) with long-range interaction decaying as r(-(d+sigma)) (where sigma is the parameter controlling the range of the interaction), is studied by the theoretic renormalization-group approach. In dimensions d<2sigma, the initial slip exponents theta(') describing the initial increase of the order parameter, and theta for the growth of the response function, which govern the short-time scaling behaviors, are calculated to the second order in sqrt[epsilon] with epsilon=2sigma-d. The crossover between the long-range interaction and the short-range interaction, which occurs at some sigma>2, is also discussed.
The aging behavior of the random n-vector model with long-range interaction decaying as r-(d+σ) (where d is the dimensionality), is investigated by the theoretic renormalization-group approach. The system initially disordered at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with model A dynamics. The aging properties are studied by the short-time expansions. The scaling behavior of two-time response and correlation functions are obtained in a frame of the expansion in ∊ = 2σ-d. In dimensions d < 2σ, the long-time limit of the critical fluctuation dissipation ratio X∞ is calculated up to one-loop order. The simulation of X∞ is discussed.