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

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