How soon after a zero-temperature quench is the fate of the Ising model sealed?

Abstract

We study the transient between a fully disordered initial condition and a percolating structure in the low-temperature non-conserved order parameter dynamics of the bi-dimensional Ising model. We show that a stable structure of spanning clusters establishes at a time $t_p \simeq L^{\alpha_p}$. Our numerical results yield $\alpha_p=0.50(2)$ for the square and kagome, $\alpha_p=0.33(2)$ for the triangular and $\alpha_p=0.38(5)$ for the bowtie-a lattices.We generalise the dynamic scaling hypothesis to take into account this new time-scale. We discuss the implications of these results for other non-equilibrium processes.