Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach

Details Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach

1995-10-13

arxiv.org/abs/cond-mat/9510077v1

Nucl. Phys. B 464 [FS] (1996) 512

Physics

Condensed Matter

27 pages, 7 postscript figures, REVTEX 3.0, submitted to Nucl. Phys. B

Scientific paper

10.1016/0550-3213(96)00012-0

We study how the finite-sized n-component model A with periodic boundary conditions relaxes near its bulk critical point from an initial nonequilibrium state with short-range correlations. Particular attention is paid to the universal long-time traces that the initial condition leaves. An approach based on renormalization-group improved perturbation theory in 4-epsilon space dimensions and a nonperturbative treatment of the q=0 mode of the fluctuating order-parameter field is developed. This leads to a renormalized effective stochastic equation for this mode in the background of the other q=0 modes; we explicitly derive it to one-loop order, show that it takes the expected finite-size scaling form at the fixed point, and solve it numerically. Our results confirm for general n that the amplitude of the magnetization density m(t) in the linear relaxation-time regime depends on the initial magnetization in the universal fashion originally found in our large-$n$ analysis [J.\ Stat. Phys. 73 (1993) 1]. The anomalous short-time power-law increase of m(t) also is recovered. For n=1, our results are in fair agreement with recent Monte Carlo simulations by Li, Ritschel, and Zheng [J. Phys. A 27 (1994) L837] for the three-dimensional Ising model.

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