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Zeroes of the triangular Potts model partition function: a conjectured distribution

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  • Anglès d'Auriac, J.C.
  • Maillard, J.M.
  • Rollet, G.
  • Wu, F.Y.

Abstract

We consider the q-state Potts model on the triangular lattice with two- and three-site interactions in alternate triangular faces, and determine zeroes of the partition function numerically in the case of pure three-site interactions. On the basis of a rigorous reciprocal symmetry and results on the zeroes for finite lattices, we conjecture that zeroes of the partition function of the triangular Potts model with pure three-site interactions in alternate triangular faces lie on a circle and a segment of the negative real axis. It is shown that the conjecture holds for q = 2, and that it reproduces the known critical point for general q, including the q = 1 site percolation.

Suggested Citation

  • Anglès d'Auriac, J.C. & Maillard, J.M. & Rollet, G. & Wu, F.Y., 1994. "Zeroes of the triangular Potts model partition function: a conjectured distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(3), pages 441-453.
    • Handle: RePEc:eee:phsmap:v:206:y:1994:i:3:p:441-453
    DOI: 10.1016/0378-4371(94)90316-6
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    References listed on IDEAS

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    1. Unknown, 1978. "Facilities for Insect Research and Production," Technical Bulletins 157863, United States Department of Agriculture, Economic Research Service.
    2. Stephenson, John & Couzens, Rodney, 1984. "Partition function zeros for the two-dimensional Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(1), pages 201-210.
    3. Hans Künzi, 1978. "Kommentar zu Hill "Betriebswirtschaftliche Führungs- und Anreizmodelle"," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 114(III), pages 645-647, September.
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