Short-time dynamics in phase-ordering kinetics

TL;DR

This paper investigates the short-time dynamics of the 2D Blume-Capel model, confirming theoretical predictions for critical initial slip exponents at both critical and tricritical points, and validating short-time scaling in phase-ordering kinetics.

Contribution

It provides numerical estimates of initial slip exponents at critical and tricritical points and confirms the validity of short-time dynamics in phase-ordering kinetics for the 2D Blume-Capel model.

Findings

Critical initial slip exponent at critical point: 0.190(5)

Initial slip exponent at tricritical point: -0.542(5)

Short-time dynamics validated in phase-ordering kinetics

Abstract

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 $\Theta=0.190({5})$ and $\Theta=-0.542({5})$, 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 $\Theta=0.39({1})$ in agreement with the scaling relation $\lambda=d-2\Theta$.