Transfer Matrices and PartitionFunction Zeros for Antiferromagnetic Potts Models. IV. Chromatic Polynomial with Cyclic Boundary Conditions
Abstract
We study the chromatic polynomial P _{ G }( q) for m× n square and triangularlattice strips of widths 2≤ m ≤ 8 with cyclic boundary conditions. This polynomial gives the zerotemperature limit of the partition function for the antiferromagnetic qstate Potts model defined on the lattice G. We show how to construct the transfer matrix in the FortuinKasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex qplane in the limit n→∞. We find that the different phases that appear in this model can be characterized by a topological parameter. We also compute the bulk and surface free energies and the central charge.
 Publication:

Journal of Statistical Physics
 Pub Date:
 February 2006
 DOI:
 10.1007/s1095500580778
 arXiv:
 arXiv:condmat/0407444
 Bibcode:
 2006JSP...122..705J
 Keywords:

 Chromatic polynomial;
 antiferromagnetic Potts model;
 triangular lattice;
 square lattice;
 transfer matrix;
 FortuinKasteleyn representation;
 Beraha numbers;
 conformal field theory;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Lattice;
 Mathematics  Combinatorics
 EPrint:
 55 pages (LaTeX2e). Includes tex file, three sty files, and 22 Postscript figures. Also included are Mathematica files transfer4_sq.m and transfer4_tri.m. Journal version