Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities
Statistical Mechanics
2014-01-03 v2
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.
Keywords
Cite
@article{arxiv.1208.2944,
title = {Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities},
author = {J. Olejarz and P. L. Krapivsky and S. Redner},
journal= {arXiv preprint arXiv:1208.2944},
year = {2014}
}
Comments
4 pages, 4 figure, 2-column revtex4 format. Revision contains material about the TDGL and is nearly identical to the final published version