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Title: Potts-model critical manifolds revisited

Journal Article · · Journal of Physics. A, Mathematical and Theoretical
 [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. PSL Research Univ., Paris (France); Sorbonne Univ., Paris (France)
+ Show Author Affiliations

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.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1399717
Report Number(s):
LLNL-JRNL-679200
Journal Information:
Journal of Physics. A, Mathematical and Theoretical, Vol. 49, Issue 12; ISSN 1751-8113
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

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Cited By (1)

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

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97 MATHEMATICS AND COMPUTING