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Algorithms for the ferromagnetic Potts model on expanders

  • Charlie Carlson
  • , Ewan Davies
  • , Nicolas Fraiman
  • , Alexandra Kolla
  • , Aditya Potukuchi
  • , Corrine Yap
  • Colorado State University
  • University of North Carolina at Chapel Hill
  • University of California at Santa Cruz
  • York University Toronto
  • Rutgers - The State University of New Jersey, New Brunswick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

We give algorithms for approximating the partition function of the ferromagnetic Potts model on d-regular expanding graphs. We require much weaker expansion than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models, using extremal graph theory and applications of Karger's algorithm to counting cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We believe that these methods can shed more light on other important problems such as sub-exponential algorithms for approximate counting problems.

Original languageEnglish
Title of host publicationProceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022
PublisherIEEE Computer Society
Pages344-355
Number of pages12
ISBN (Electronic)9781665455190
DOIs
StatePublished - 2022
Event63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022 - Denver, United States
Duration: Oct 31 2022Nov 3 2022

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2022-October
ISSN (Print)0272-5428

Conference

Conference63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022
Country/TerritoryUnited States
CityDenver
Period10/31/2211/3/22

Keywords

  • approximate counting
  • approximate sampling
  • expander graphs
  • Potts model
  • random cluster model

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