License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.STACS.2016.51
URN: urn:nbn:de:0030-drops-57526
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5752/
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Lu, Pinyan ; Yang, Kuan ; Zhang, Chihao

FPTAS for Hardcore and Ising Models on Hypergraphs

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Abstract

Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their interactions with their macroscopic and statistical properties of materials such as energy, entropy, ferromagnetism, etc. If each local interaction of the system involves only two particles, the system can be described by a graph. In this case, fully polynomial-time approximation scheme (FPTAS) for computing the partition function of both hardcore and anti-ferromagnetic Ising model was designed up to the uniqueness condition of the system. These result are the best possible since approximately computing the partition function beyond this threshold is NP-hard. In this paper, we generalize these results to general physics systems, where each local interaction may involves multiple particles. Such systems are described by hypergraphs. For hardcore model, we also provide FPTAS up to the uniqueness condition, and for anti-ferromagnetic Ising model, we obtain FPTAS under a slightly stronger condition.

BibTeX - Entry

@InProceedings{lu_et_al:LIPIcs:2016:5752,
  author =	{Pinyan Lu and Kuan Yang and Chihao Zhang},
  title =	{{FPTAS for Hardcore and Ising Models on Hypergraphs}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5752},
  URN =		{urn:nbn:de:0030-drops-57526},
  doi =		{10.4230/LIPIcs.STACS.2016.51},
  annote =	{Keywords: hard-core model, ising model, hypergraph, spatial mixing, correlation decay}
}

Keywords: hard-core model, ising model, hypergraph, spatial mixing, correlation decay
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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