# Critical percolation in the dynamics of the 2d ferromagnetic Ising model

## TL;DR

This paper investigates the early-time dynamics of the 2D ferromagnetic Ising model after a quench, revealing rapid approach to critical percolation and analyzing the scaling and geometry dependence of the process.

## Contribution

It identifies a new growing length scale associated with critical percolation, distinct from curvature-driven coarsening, and explores its dependence on lattice geometry.

## Key findings

- Rapid approach to critical percolation time-scale diverging with system size
- Identification of a new growing length scale in the dynamics
- Dependence of the length scale on lattice coordination

## Abstract

We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order parameter. We confirm the rapid approach to random critical percolation in a time-scale that diverges with the system size but is much shorter than the equilibration time. We study the scaling properties of the evolution towards critical percolation and we identify an associated growing length, different from the curvature driven one. By working with the model defined on square, triangular and honeycomb microscopic geometries we establish the dependence of this growing length on the lattice coordination. We discuss the interplay with the usual coarsening mechanism and the eventual fall into and escape from metastability.