Dynamical cluster size heterogeneity

Abstract

Only recently the essential role of the percolation critical point has been considered on the dynamical properties of connected regions of aligned spins (domains) after a sudden temperature quench. In equilibrium, it is possible to resolve the contribution to criticality by the thermal and percolative effects (on finite lattices, while in the thermodynamic limit they merge at a single critical temperature) by studying the cluster size heterogeneity, $H_{\mathrm{eq}}(T)$, a measure of how different the domains are in size. We here extend this equilibrium measure and study its temporal evolution, $H(t)$, after driving the system out of equilibrium by a sudden quench in temperature. We show that this single parameter is able to detect and well separate the different time regimes, related to the two time scales in the problem, the short, percolative and the long, coarsening one.

7 pages

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• Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model
• A branching random-walk model of disease outbreaks and the percolation backbone
• Field-induced freezing in the unfrustrated Ising antiferromagnet