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 two-dimensional Ising model. We show that a stable structure of spanning clusters establishes at a time . Our numerical results yield for the square and kagome lattices, for the triangular and 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.