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URN: urn:nbn:de:0030-drops-47428
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The Complexity of Ferromagnetic Two-spin Systems with External Fields

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Abstract

We study the approximability of computing the partition function for ferromagnetic two-state spin systems. The remarkable algorithm by Jerrum and Sinclair showed that there is a fully polynomial-time randomized approximation scheme (FPRAS) for the special ferromagnetic Ising model with any given uniform external field. Later, Goldberg and Jerrum proved that it is #BIS-hard for Ising model if we allow inconsistent external fields on different nodes. In contrast to these two results, we prove that for any ferromagnetic two-state spin systems except the Ising model, there exists a threshold for external fields beyond which the problem is #BIS-hard, even if the external field is uniform.

BibTeX - Entry

@InProceedings{liu_et_al:LIPIcs:2014:4742,
  author =	{Jingcheng Liu and Pinyan Lu and Chihao Zhang},
  title =	{{The Complexity of Ferromagnetic Two-spin Systems with External Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{843--856},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4742},
  URN =		{urn:nbn:de:0030-drops-47428},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.843},
  annote =	{Keywords: Spin System, #BIS-hard, FPRAS}
}

Keywords: Spin System, #BIS-hard, FPRAS
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Issue date: 2014
Date of publication: 2014


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