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.

5 pages, 6 figures + supplemental material (2 pages, 1 figure), version 2: new co-author, extended manuscript

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