TY - JOUR

T1 - Transfer matrices and partition-function zeros for zntiferromagnetic potts models

T2 - VV. further results for the square-lattice chromatic polynomial

AU - Salas, Jesús

AU - Sokal, Alan D.

N1 - Funding Information:
The authors’ research was supported in part by US National Science Foundation grants PHY-0116590 and PHY-0424082 (A.D.S.), and by Spanish MEC grants MTM2005-08618, MTM2008-03020, and FIS2004-03767 (J.S.).

PY - 2009/4

Y1 - 2009/4

N2 - We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q -47 (resp. q -46). Finally, we compute chromatic roots for strips of widths 12 with free boundary conditions and locate roughly the limiting curves.

AB - We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q -47 (resp. q -46). Finally, we compute chromatic roots for strips of widths 12 with free boundary conditions and locate roughly the limiting curves.

KW - Antiferromagnetic Potts model

KW - Beraha-Kahane-Weiss theorem

KW - Chromatic polynomial

KW - Chromatic root

KW - Finite-lattice method

KW - Fortuin-Kasteleyn representation

KW - Large-q expansion

KW - One-dimensional polymer model

KW - Square lattice

KW - Transfer matrix

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U2 - 10.1007/s10955-009-9725-1

DO - 10.1007/s10955-009-9725-1

M3 - Article

AN - SCOPUS:67349158736

VL - 135

SP - 279

EP - 373

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -