Pottsmodel critical manifolds revisited
We compute the critical polynomials for the qstate 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 Pottsmodel critical manifolds in the real (q; v) plane. In the two most favourable cases, we find now the kagomelattice 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 BerkerKadano phase for the lattices studied.
 Authors:

^{[1]};
^{[2]}
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 PSL Research Univ., Paris (France); Sorbonne Univ., Paris (France)
 Publication Date:
 Report Number(s):
 LLNLJRNL679200
Journal ID: ISSN 17518113
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Physics. A, Mathematical and Theoretical
 Additional Journal Information:
 Journal Volume: 49; Journal Issue: 12; Journal ID: ISSN 17518113
 Publisher:
 IOP Publishing
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1399717
Scullard, Christian R., and Jacobsen, Jesper Lykke. Pottsmodel critical manifolds revisited. United States: N. p.,
Web. doi:10.1088/17518113/49/12/125003.
Scullard, Christian R., & Jacobsen, Jesper Lykke. Pottsmodel critical manifolds revisited. United States. doi:10.1088/17518113/49/12/125003.
Scullard, Christian R., and Jacobsen, Jesper Lykke. 2016.
"Pottsmodel critical manifolds revisited". United States.
doi:10.1088/17518113/49/12/125003. https://www.osti.gov/servlets/purl/1399717.
@article{osti_1399717,
title = {Pottsmodel critical manifolds revisited},
author = {Scullard, Christian R. and Jacobsen, Jesper Lykke},
abstractNote = {We compute the critical polynomials for the qstate 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 = eK1 is determined numerically at q = 1 for bases of size 8 8. This leads to improved results for bond percolation thresholds, and for the Pottsmodel critical manifolds in the real (q; v) plane. In the two most favourable cases, we find now the kagomelattice 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 BerkerKadano phase for the lattices studied.},
doi = {10.1088/17518113/49/12/125003},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 12,
volume = 49,
place = {United States},
year = {2016},
month = {2}
}