Dynamical cluster size heterogeneity

TL;DR

This paper introduces a dynamic measure called cluster size heterogeneity to analyze the evolution of domain structures in spin systems after a temperature quench, revealing distinct time regimes related to percolation and coarsening.

Contribution

It extends the equilibrium cluster size heterogeneity measure to out-of-equilibrium dynamics, enabling detection of different temporal regimes after a temperature quench.

Findings

H(t) effectively distinguishes between percolative and coarsening regimes.

The measure captures the transition between different dynamical phases.

It provides insights into the temporal evolution of domain structures.

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, $H_{\scriptstyle\rm eq}(T)$, 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.