A morphological study of cluster dynamics between critical points

TL;DR

This paper investigates the morphological evolution of spin and Fortuin-Kasteleyn clusters in a 2D Ising model after a quench between critical points, revealing scale-dependent properties during non-equilibrium dynamics.

Contribution

It provides a detailed numerical analysis of cluster morphology during critical point quenches, highlighting scale-dependent properties and suggesting potential for analytical descriptions.

Findings

Small-scale properties reflect the target critical point.

Large-scale properties retain initial critical point characteristics.

Similarities with sub-critical quenches observed.

Abstract

We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising model and we use numerical methods to characterize the morphological and statistical properties of spin and Fortuin-Kasteleyn clusters during the critical evolution. The analysis of the dynamics of an out of equilibrium interface is also performed. We show that the small scale properties, smaller than the target critical growing length $\xi(t) \sim t^{1/z}$ with $z$ the dynamic exponent, are characterized by equilibrium at the working critical point, while the large scale properties, larger than the critical growing length, are those of the initial critical point. These features are similar to what was found for sub-critical quenches. We argue that quenches between critical points could be amenable to a more detailed analytical description.