License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.96
URN: urn:nbn:de:0030-drops-125036
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12503/
Go to the corresponding LIPIcs Volume Portal

Shao, Shuai ; Sun, Yuxin

Contraction: A Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems

pdf-format:
LIPIcs-ICALP-2020-96.pdf (0.6 MB)

Abstract

We study complex zeros of the partition function of 2-spin systems, viewed as a multivariate polynomial in terms of the edge interaction parameters and the uniform external field. We obtain new zero-free regions in which all these parameters are complex-valued. Crucially based on the zero-freeness, we are able to extend the existence of correlation decay to these complex regions from real parameters. As a consequence, we obtain an FPTAS for computing the partition function of 2-spin systems on graphs of bounded degree for these parameter settings. We introduce the contraction property as a unified sufficient condition to devise FPTAS via either Weitz’s algorithm or Barvinok’s algorithm. Our main technical contribution is a very simple but general approach to extend any real parameter of which the 2-spin system exhibits correlation decay to its complex neighborhood where the partition function is zero-free and correlation decay still exists. This result formally establishes the inherent connection between two distinct notions of phase transition for 2-spin systems: the existence of correlation decay and the zero-freeness of the partition function via a unified perspective, contraction.

BibTeX - Entry

@InProceedings{shao_et_al:LIPIcs:2020:12503,
  author =	{Shuai Shao and Yuxin Sun},
  title =	{{Contraction: A Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{96:1--96:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12503},
  URN =		{urn:nbn:de:0030-drops-125036},
  doi =		{10.4230/LIPIcs.ICALP.2020.96},
  annote =	{Keywords: 2-Spin system, Correlation decay, Zero-freeness, Phase transition, Contraction}
}

Keywords: 2-Spin system, Correlation decay, Zero-freeness, Phase transition, Contraction
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI