Short-time dynamics in phase-ordering kinetics

Short-time dynamics in the $2D$ Blume-Capel model, with a non-conserved order-parameter and short-ranged interactions, is analysed. For non-equilibrium dynamics, both at a critical point in the $2D$ Ising universality class and at the tricritical point, we reproduce the values $\mathrm{\Theta }=0.190(5)$ and $\mathrm{\Theta }=-0.542(5)$, respectively, of the critical initial slip exponent. These agree with more early estimates and with the Janssen-Schaub-Schmittmann scaling relation. In phase-ordering kinetics, after a quench into the ordered phase, we establish the validity of short-time dynamics. In the $2D$ Ising universality class, we find $\mathrm{\Theta }=0.39(1)$ in agreement with the scaling relation $\lambda =d-2\mathrm{\Theta }$.