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arXiv · 0905.3521

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

Kipton Barros·P. L. Krapivsky·S. Redner
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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.

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Kipton Barros, P. L. Krapivsky, S. Redner. 2011-01-27. Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation. https://doi.org/10.1103/physreve.80.040101

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