How soon after a zero-temperature quench is the fate of the Ising model sealed?
1 Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE - F-75005, Paris, France
2 CNRS, UMR 7589, LPTHE - F-75005, Paris, France
3 Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno - via Ponte don Melillo, I-84084 Fisciano (SA), Italia
Received: 26 March 2014
Accepted: 19 May 2014
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.
PACS: 64.60.Cn – Order-disorder transformations / 64.60.ah – Percolation / 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)
© EPLA, 2014