Approximate Lifshitz law for the zero-temperature stochastic Ising in any dimension

Details Approximate Lifshitz law for the zero-temperature stochastic Ising in any dimension Approximate Lifshitz law for the zero-temperature stochastic Ising in any dimension

2011-02-17

arxiv.org/abs/1102.3466v1

Physics

Mathematical Physics

12 Pages

Scientific paper

We study the Glauber dynamics for the zero-temperature Ising model in dimension d=4 with "plus" boundary condition. We show that the time T+ needed for a hyper-cube of size L entirely filled with "minus" spins to become entirely "plus" 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 interface at equilibrium and mixing time for monotone interface extracted from [2], to get the result in higher dimension.

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