The short-time behavior of kinetic spherical model with long-ranged interactions

Abstract

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m_{0} quenched from a very high temperature to T < T_{c} is solved. In the short-time regime, the bulk order increases with a power law in both the critical and phase-ordering dynamics. To the latter dynamics, a power law for the relative order m_{r} ~ -t^{-k} is found in the intermediate time-regime. The short-time scaling relation of small m_{0} are generalized to an arbitrary m_{0} and all the time larger than t_{mic}. The characteristic functions $\varphi (b,m_0)$ for the scaling of m_{0} and $\epsilon (b,T^{\prime })$ for T'=T/T_{c} are obtained. The crossover between scaling regimes is discussed in detail.

22 pages, 3 figures

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