任意维零温随机伊辛模型的近似Lifshitz律
Approximate Lifshitz law for the zero-temperature stochastic Ising model in any dimension
摘要：
本文研究了d=4维零温伊辛模型在“正”边界条件下的Glauber动力学，设T+是一个尺寸为L的完全充满“负”自旋的超立方体到完全充满“正”自旋所需的时间.我们证明了T+是O（L^2（log L）^c）对于某个常数c，不依赖于维数。这为所谓的“利夫希茨定律”T+ = O（L^2）[5，3]提供了进一步的严格证明。我们证明的关键是利用我们在三维问题上所掌握的详细知识：[2]中关于单调界面在平衡态的涨落和单调界面动力学的混合时间的结果，来得到更高维的结果。
英文摘要：
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.
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