Combinatorial criteria for uniqueness of Gibbs measures
Combinatorial criteria for uniqueness of Gibbs measures
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DOI：
10.1002/rsa.20073
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发表时间：
2005-12
影响因子：
1
通讯作者：
Dror Weitz
中科院分区：
文献类型：
--
作者：
Dror Weitz
通过给出任意图上模型的任意有限大小的条件，我们推广了已知的统计物理模型中Gibbs测度唯一的条件。我们给出了两个对偶条件，一个要求对站点的总影响很小，另一个要求站点的总影响很小。我们的证明本质上是组合的，并使用了离散马尔可夫链的分析工具，特别是路径耦合方法。文中还讨论了我们的条件对与模型有关的自然马氏链的混合时间的影响。我们还给出了一些条件成立的模型的例子。©2005威利期刊公司随机结构。ALG，2005
We generalize previously known conditions for uniqueness of the Gibbs measure in statistical physics models by presenting conditions of any finite size for models on any underlying graph. We give two dual conditions, one requiring that the total influence on a site is small, and the other that the total influence of a site is small. Our proofs are combinatorial in nature and use tools from the analysis of discrete Markov chains, in particular the path coupling method. The implications of our conditions for the mixing time of natural Markov chains associated with the models are discussed as well. We also present some examples of models for which the conditions hold. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005