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

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

2009-05-21

arxiv.org/abs/0905.3521v2

Phys. Rev. E 80, 040101 (2009)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, 2-column revtex4 format; latest revision fixes small typos in some formulae

Scientific paper

10.1103/PhysRevE.80.040101

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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