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

TL;DR

This paper analytically investigates the short-time dynamics of the kinetic spherical model with long-range interactions after a quench, revealing power-law growth of order parameters and scaling relations for various initial conditions.

Contribution

It provides exact solutions for the short-time behavior of the kinetic spherical model with long-range interactions, including generalized scaling relations for arbitrary initial order.

Findings

Power-law increase of bulk order in short-time regime

Power-law decay of relative order in intermediate time-regime

Derived scaling functions for initial order and temperature ratios

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 $\phi (b,m_{0})$ 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.