Approximate Lifshitz law for the zero-temperature stochastic Ising model in any dimension
Abstract
We study the Glauber dynamics for the zero-temperature Ising model in dimension d=4 with "plus" boundary condition.Let T+ be the time needed for an hypercube of size L entirely filled with "minus" spins to become entirely "plus". We prove that T+ is O(L^2(log L)^c) for some constant c, not depending on the dimension. This brings further rigorous justification for the so-called "Lifshitz law" T+ = O(L^2) [5, 3] conjectured on heuristic grounds. The key point of our proof is to use the detail knowledge that we have on the three-dimensional problem: results for fluctuation of monotone interfaces at equilibrium and mixing time for monotone interfaces dynamics extracted from [2], to get the result in higher dimension.
Keywords
Cite
@article{arxiv.1102.3466,
title = {Approximate Lifshitz law for the zero-temperature stochastic Ising model in any dimension},
author = {Hubert Lacoin},
journal= {arXiv preprint arXiv:1102.3466},
year = {2012}
}
Comments
15 Pages, 2 figures, accepted for publication in Communication in Mathematical Physics