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

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.

4 pages, 4 figure, 2-column revtex4 format. Revision contains material about the TDGL and is nearly identical to the final published version

References in corpus (7)

• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• Percolation Crossing Formulas and Conformal Field Theory
• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Zero-Temperature Freezing in Three-Dimensional Kinetic Ising Model
• Ising Ferromagnet: Zero-Temperature Dynamic Evolution
• On Crossing Event Formulas in Critical Two-Dimensional Percolation

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