- m at . s of t ] 1 2 N ov 1 99 9 The short - time behavior of kinetic spherical model with long - ranged interactions ∗

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m0 quenched from a very high temperature to T (≤ Tc) 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 mr ∼ −t−k is found in the intermediate time-regime. The short-time scaling relations of small m0 are generalized to an arbitrary m0 and all the time larger than tmic. The characteristic functions φ(b,m0) for the scaling of m0 and ǫ(b, T ′) for T ′ = T/Tc are obtained. The crossover between scaling regimes is discussed in detail.