Chaotic Size Dependence in the Ising Model with Random Boundary Conditions
Chaotic Size Dependence in the Ising Model with Random Boundary Conditions
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DOI：
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发表时间：
2001-08
影响因子：
0.2
通讯作者：
van Aernout Enter;I. Medved’;Karel Netočný
中科院分区：
文献类型：
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作者：
van Aernout Enter;I. Medved’;Karel Netočný
本文研究了具有一类随机边界条件的最近邻Ising模型，这些边界条件选自对称同分布的随机边界条件。分布我们证明了4维和更高的维度，几乎可以肯定的是，唯一的极限点的一系列增加立方体是加和减状态。对于d=2和d=3，我们证明了一个类似的结果，稀疏序列的增加立方体。这个问题是由纽曼和斯坦提出的。我们的结果意味着Newman-Stein亚态集中在正态和负态。
We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.