Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model

TL;DR

This paper investigates the critical percolation properties of interfaces in a 2D ferromagnetic Ising model during slow cooling, confirming theoretical predictions about out-of-equilibrium dynamics and scaling behaviors.

Contribution

It demonstrates that equilibrium interfaces exhibit critical percolation fractal dimensions and characterizes the dynamic scaling during slow cooling, linking out-of-equilibrium behavior to critical phenomena.

Findings

Interfaces have critical percolation fractal dimension over wide scales

Out-of-equilibrium temperature depends on cooling rate as per Kibble-Zurek

Dynamic length scales follow predicted scaling laws

Abstract

We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble-Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the growing length reached when the system fell out of equilibrium.