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Recent results on the short-time behaviors of a few models possessing a common feature of long-ranged interaction will be summarized. For the disorder initial state, the initial order increase is observed for each model in a heat-bath at the critical temperature. The dynamic exponents are calculated. For arbitrary initial order and environment temperature, universal characteristic functions are introduced in order to generalize the scaling relations. Remarkable consistence between the theoretic renormalization group results and the simulations are found in the long-range regime.

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.

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