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
SN - 0022-4715
VL - 135
SP - 279
EP - 373
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
ER -