Short-time behavior of the kinetic spherical model with long-ranged interactions

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m(0) quenched from a very high temperature to T (less than or equal to 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) similar to -t(-k) found in the intermediate time-regime. The short-time scaling relations of small m(0) are generalized to an arbitrary m(0) and all the time larger than t(mic). The characteristic functions phi(b, m(0)) for the scaling of m(0) and epsilon(b, T') for T' = T/T-c are obtained. The crossover between scaling regimes is discussed in detail.