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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Fate of 2D kinetic ferromagnets and critical percolation crossing probabilities
J Olejarz1, P L Krapivsky, S Redner
1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Abstract:
We present evidence for a deep connection between the zero-temperature coarsening of both the two-dimensional time-dependent Ginzburg-Landau equation and the kinetic Ising model with critical continuum percolation. In addition to reaching the ground state, the time-dependent Ginzburg-Landau equation and kinetic Ising model can 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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