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Journal of Physics A Mathematical and General

Short-time critical behaviour of anisotropic cubic systems with long-range interaction

Yuan Chen, Zhibing Li

Published Feb 19, 2001• 12 citations
Publisher

Abstract

The renormalization group approach is applied to the study of the short-time critical behaviour of the d -dimensional n -component anisotropic cubic spin systems with long-range interaction of the form p σ s p s - p in momentum space. Firstly, the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents θ' and θ of the order parameter and the response function, respectively, are calculated to the second order in = 2σ- d . For 1⩽ d <2σ and n > n c , the cubic anisotropy affects the short-time critical behaviour.

DOI
10.1088/0305-4470/34/8/302

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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=4d=4d=4 dimension.
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 pσsps-p. 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. A double expansion in ∈ = 2σ-d and α = 1 -σ/2 with α of order ∈ is employed, where d is the spatial dimension. The asymptotic scaling laws and the initial slip exponents θ' and θ for the order parameter and the response function respectively are calculated to the second order in ∈ for σ close to 2.
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.
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.
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.