Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models Articles uri icon

publication date

  • April 2009

start page

  • 279

end page

  • 373

issue

  • 2

volume

  • 135

international standard serial number (ISSN)

  • 0022-4715

electronic international standard serial number (EISSN)

  • 1572-9613

abstract

  • 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 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves. Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files dataCYL.m and dataFREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phys