Out-of-equilibrium percolation transitions at finite critical times after quenches across magnetic first-order transitions

TL;DR

This paper demonstrates an out-of-equilibrium percolation transition in a 2D Ising system after a magnetic field quench across a first-order transition, characterized by a finite critical time and unique scaling behaviors.

Contribution

It reveals a novel dynamic percolation transition occurring at finite times after quenches across first-order magnetic transitions, with detailed scaling and critical behavior analysis.

Findings

Percolation transition occurs at a finite critical time after the quench.

The transition exhibits finite-size scaling similar to random percolation.

The critical time depends exponentially on the magnetic field strength.

Abstract

We show that an out-of-equilibrium percolation transition occurs after quenching ferromagnetic Ising-like systems across their magnetic first-order transitions. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature first-order transition line by a quench of the magnetic field $h$ from $h_i<0$ to $h>0$. In the thermodynamic limit and for finite values of $h$, the post-quench evolution under a purely relaxational dynamics is characterized by a dynamic transition at a finite critical time $t_c(h)$ from the metastable negatively magnetized phase to the positive one, marked by the percolation of the largest clusters of positive and negative spins. This out-of-equilibrium percolation transition displays a finite-size scaling behavior as in the standard random-percolation case. However, while the fractal dimension of the percolating clusters is consistent with the random-percolation value, the exponent controlling the approach to criticality differs and depends on $h$. We also show that the percolation critical behavior is related to the spinodal-like behavior of the magnetization in the small-$h$ limit, which implies that the percolation time $t_c(h)$ exhibits a spinodal-like exponential dependence on $h$.