Approximating partition functions of the two-state spin system

Authors:
Jinshan Zhang;Heng Liang;Fengshan Bai
Affiliations:
Department of Computer Science, University of Liverpool, UK;Department of Mathematical Sciences, Tsinghua University, China;Department of Mathematical Sciences, Tsinghua University, China
Venue:
Information Processing Letters
Year:
2011

Citing 5
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Abstract

Two-state spin system is a classical topic in statistical physics. We consider the problem of computing the partition function of the system on a bounded degree graph. Based on the self-avoiding tree, we prove the system exhibits strong correlation decay under the condition that the absolute value of inverse temperature is small. Due to strong correlation decay property, an FPTAS for the partition function is presented and uniqueness of Gibbs measure of the two-state spin system on a bounded degree infinite graph is proved, under the same condition. This condition is sharp for Ising model.