Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions

Jesper Lykke Jacobsen, Jesus Salas 1

Journal of Statistical Physics 122 (2006) 705-760

We study the chromatic polynomial P_G(q) for m \times n square- and triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. 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.

  • 1. Grupo de Modelizacion, Simulacion Numerica y Matematica Industrial,
    Universidad Carlos III de Madrid