Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation

TL;DR

This paper analytically predicts the probability of a 2D Ising ferromagnet forming stripe states after a quench, using percolation theory, and confirms these predictions with simulations, advancing understanding of coarsening dynamics.

Contribution

It introduces an analytical method linking percolation theory to coarsening dynamics in 2D ferromagnets, predicting stripe state probabilities based on aspect ratio and boundary conditions.

Findings

Predicted stripe state probabilities match simulation results.

Derived analytical formulas for crossing probabilities in critical percolation.

Applicable to coarsening dynamics of non-conserved scalar fields in two dimensions.

Abstract

When a two-dimensional Ising ferromagnet is quenched from above the critical temperature to zero temperature, the system eventually converges to either a ground state (all spins aligned) or an infinitely long-lived metastable stripe state. By applying results from percolation theory, we analytically determine the probability to reach the stripe state as a function of the aspect ratio and the form of the boundary conditions. These predictions agree with simulation results. Our approach generally applies to coarsening dynamics of non-conserved scalar fields in two dimensions.