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arXiv · 1208.2944

Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities

J. Olejarz·P. L. Krapivsky·S. Redner
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Abstract

We present evidence for a deep connection between the zero-temperature coarsening of the two-dimensional kinetic Ising model (KIM) and critical continuum percolation. In addition to reaching the ground state, the KIM can also fall into a variety of topologically distinct metastable stripe states. The probability to reach a stripe state that winds a times horizontally and b times vertically on a square lattice with periodic boundary conditions equals the corresponding exactly-solved critical percolation crossing probability P_{a,b} for a spanning path with winding numbers a and b.

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J. Olejarz, P. L. Krapivsky, S. Redner. 2013-12-31. Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities. https://doi.org/10.1103/physrevlett.109.195702

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