License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.66
URN: urn:nbn:de:0030-drops-141353
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14135/
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Friedrich, Tobias ; Göbel, Andreas ; Krejca, Martin S. ; Pappik, Marcus

A Spectral Independence View on Hard Spheres via Block Dynamics

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LIPIcs-ICALP-2021-66.pdf (0.7 MB)


Abstract

The hard-sphere model is one of the most extensively studied models in statistical physics. It describes the continuous distribution of spherical particles, governed by hard-core interactions. An important quantity of this model is the normalizing factor of this distribution, called the partition function. We propose a Markov chain Monte Carlo algorithm for approximating the grand-canonical partition function of the hard-sphere model in d dimensions. Up to a fugacity of λ < e/2^d, the runtime of our algorithm is polynomial in the volume of the system. This covers the entire known real-valued regime for the uniqueness of the Gibbs measure.
Key to our approach is to define a discretization that closely approximates the partition function of the continuous model. This results in a discrete hard-core instance that is exponential in the size of the initial hard-sphere model. Our approximation bound follows directly from the correlation decay threshold of an infinite regular tree with degree equal to the maximum degree of our discretization. To cope with the exponential blow-up of the discrete instance we use clique dynamics, a Markov chain that was recently introduced in the setting of abstract polymer models. We prove rapid mixing of clique dynamics up to the tree threshold of the univariate hard-core model. This is achieved by relating clique dynamics to block dynamics and adapting the spectral expansion method, which was recently used to bound the mixing time of Glauber dynamics within the same parameter regime.

BibTeX - Entry

@InProceedings{friedrich_et_al:LIPIcs.ICALP.2021.66,
  author =	{Friedrich, Tobias and G\"{o}bel, Andreas and Krejca, Martin S. and Pappik, Marcus},
  title =	{{A Spectral Independence View on Hard Spheres via Block Dynamics}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{66:1--66:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14135},
  URN =		{urn:nbn:de:0030-drops-141353},
  doi =		{10.4230/LIPIcs.ICALP.2021.66},
  annote =	{Keywords: Hard-sphere Model, Markov Chain, Partition Function, Gibbs Distribution, Approximate Counting, Spectral Independence}
}

Keywords: Hard-sphere Model, Markov Chain, Partition Function, Gibbs Distribution, Approximate Counting, Spectral Independence
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021


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