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 $t_p \simeq L^{\alpha_p}$ . Our numerical results yield $\alpha_p=0.50(2)$ for the square and kagome lattices, $\alpha_p=0.33(2)$ 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.

### 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 $t_p \simeq L^{\alpha_p}$ . Our numerical results yield $\alpha_p=0.50(2)$ for the square and kagome lattices, $\alpha_p=0.33(2)$ 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.
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2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4522058
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