TY - JOUR

T1 - Transfer matrices for the zero-temperature Potts antiferromagnet on cyclic and Möbius lattice strips

AU - Chang, Shu Chiuan

AU - Shrock, Robert

N1 - Funding Information:
We thank J. Salas for discussions on transfer matrix methods during the work for Refs. [60,61] , A. Sokal for related discussions, and N. Biggs for discussion on sieve methods. The research of R.S. was partially supported by the NSF grant PHY-00-98527. The research of S.C.C. was partially supported by the Nishina and Inoue Foundations, and he thanks Prof. M. Suzuki for further support. The NCTS Taipei address for S.C.C. applies after April 12, 2004, until July 31, 2004; the address for S.C.C. as of Aug. 1, 2004 is Physics Dept., National Cheng Kung University, Tainan, Taiwan, email: scchang@mail.ncku.edu.tw.

PY - 2005/2/15

Y1 - 2005/2/15

N2 - We present transfer matrices for the zero-temperature partition function of the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and Möbius strips of the square, triangular, and honeycomb lattices of width Ly and arbitrarily great length Lx. We relate these results to our earlier exact solutions for square-lattice strips with Ly = 3, 4, 5, triangular-lattice strips with Ly = 2, 3, 4, and honeycomb-lattice strips with Ly = 2, 3 and periodic or twisted periodic boundary conditions. We give a general expression for the chromatic polynomial of a Möbius strip of a lattice A and exact results for a subset of honeycomb-lattice transfer matrices, both of which are valid for arbitrary strip width Ly. New results are presented for the Ly = 5 strip of the triangular lattice and the Ly = 4 and Ly = 5 strips of the honeycomb lattice. Using these results and taking the infinite-length limit Lx → ∞, we determine the continuous accumulation locus of the zeros of the above partition function in the complex q plane, including the maximal real point of nonanalyticity of the degeneracy per site, W as a function of q.

AB - We present transfer matrices for the zero-temperature partition function of the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and Möbius strips of the square, triangular, and honeycomb lattices of width Ly and arbitrarily great length Lx. We relate these results to our earlier exact solutions for square-lattice strips with Ly = 3, 4, 5, triangular-lattice strips with Ly = 2, 3, 4, and honeycomb-lattice strips with Ly = 2, 3 and periodic or twisted periodic boundary conditions. We give a general expression for the chromatic polynomial of a Möbius strip of a lattice A and exact results for a subset of honeycomb-lattice transfer matrices, both of which are valid for arbitrary strip width Ly. New results are presented for the Ly = 5 strip of the triangular lattice and the Ly = 4 and Ly = 5 strips of the honeycomb lattice. Using these results and taking the infinite-length limit Lx → ∞, we determine the continuous accumulation locus of the zeros of the above partition function in the complex q plane, including the maximal real point of nonanalyticity of the degeneracy per site, W as a function of q.

UR - http://www.scopus.com/inward/record.url?scp=10444251814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10444251814&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2004.08.010

DO - 10.1016/j.physa.2004.08.010

M3 - Article

AN - SCOPUS:10444251814

SN - 0378-4371

VL - 346

SP - 400

EP - 450

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 3-4

ER -