Counting Without Sampling: Asymptotics of the Log-Partition Function for Certain Statistical Physics Models
Counting Without Sampling: Asymptotics of the Log-Partition Function for Certain Statistical Physics Models
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DOI：
10.1002/rsa.20236
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发表时间：
2008-12-01
影响因子：
1
通讯作者：
Gamarnik, David
中科院分区：
文献类型：
--
作者：
Bandyopadhyay, Antar;Gamarnik, David
在本文中，我们提出了计算某些统计物理模型在某些类型的有限图上的配分函数（自由能）的对数的渐近值的新方法，当底层图的大小趋于无穷时。考虑的两个模型是活动参数lambda较小时的硬核（独立集）模型，以及Potts （q-coloring）模型。我们只考虑周长较大的图。特别地，我们证明了任意大周长的r正则图的独立集数的对数在重新标度时近似为常数
In this article we propose new methods for computing the asymptotic value for the logarithm of the partition function (free energy) for certain statistical physics models on certain type of finite graphs, as the size of the underlying graph goes to infinity. The two models considered are the hard-core (independent set) model when the activity parameter lambda is small, and also the Potts (q-coloring) model. We only consider the graph with large girth. In particular, we prove that asympototically the logarithm of the number of independent sets of any r-regular graph with large girth when rescaled is approximately constant if r