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Title: Potts-model critical manifolds revisited

Abstract

We compute the critical polynomials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of Ref. [1] that gives us access to larger sizes than previously possible. The exact polynomials are computed for bases of size 6 6 unit cells, and the root in the temperature variable v = e K-1 is determined numerically at q = 1 for bases of size 8 8. This leads to improved results for bond percolation thresholds, and for the Potts-model critical manifolds in the real (q; v) plane. In the two most favourable cases, we find now the kagome-lattice threshold to eleven digits and that of the (3; 12 2) lattice to thirteen. Our critical manifolds reveal many interesting features in the antiferromagnetic region of the Potts model, and determine accurately the extent of the Berker-Kadano phase for the lattices studied.

Authors:
 [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. PSL Research Univ., Paris (France); Sorbonne Univ., Paris (France)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1399717
Report Number(s):
LLNL-JRNL-679200
Journal ID: ISSN 1751-8113
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Physics. A, Mathematical and Theoretical
Additional Journal Information:
Journal Volume: 49; Journal Issue: 12; Journal ID: ISSN 1751-8113
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Scullard, Christian R., and Jacobsen, Jesper Lykke. Potts-model critical manifolds revisited. United States: N. p., 2016. Web. doi:10.1088/1751-8113/49/12/125003.
Scullard, Christian R., & Jacobsen, Jesper Lykke. Potts-model critical manifolds revisited. United States. https://doi.org/10.1088/1751-8113/49/12/125003
Scullard, Christian R., and Jacobsen, Jesper Lykke. Thu . "Potts-model critical manifolds revisited". United States. https://doi.org/10.1088/1751-8113/49/12/125003. https://www.osti.gov/servlets/purl/1399717.
@article{osti_1399717,
title = {Potts-model critical manifolds revisited},
author = {Scullard, Christian R. and Jacobsen, Jesper Lykke},
abstractNote = {We compute the critical polynomials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of Ref. [1] that gives us access to larger sizes than previously possible. The exact polynomials are computed for bases of size 6 6 unit cells, and the root in the temperature variable v = eK-1 is determined numerically at q = 1 for bases of size 8 8. This leads to improved results for bond percolation thresholds, and for the Potts-model critical manifolds in the real (q; v) plane. In the two most favourable cases, we find now the kagome-lattice threshold to eleven digits and that of the (3; 122) lattice to thirteen. Our critical manifolds reveal many interesting features in the antiferromagnetic region of the Potts model, and determine accurately the extent of the Berker-Kadano phase for the lattices studied.},
doi = {10.1088/1751-8113/49/12/125003},
url = {https://www.osti.gov/biblio/1399717}, journal = {Journal of Physics. A, Mathematical and Theoretical},
issn = {1751-8113},
number = 12,
volume = 49,
place = {United States},
year = {2016},
month = {2}
}

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Cited by: 6 works
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Works referenced in this record:

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Some generalized order-disorder transformations
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Fehlerabsch�tzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus
journal, December 1964


    Works referencing / citing this record:

    The three-state Potts antiferromagnet on plane quadrangulations
    journal, July 2018