2007/03/31 by Jesper Lykke Jacobsen, Jesus Salas, Jesús Salas · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat #math.CO
paper · pdf · doi:10.1016/j.nuclphysb.2007.04.023
published as Nucl.Phys.B783:238-296,2007 · 72 pages (LaTeX2e). Includes tex file, three sty files, and 26 Postscript figures. Also included are Mathematica files transfer6_sq.m and transfer6_tri.m. Final version to appear in Nucl. Phys. B
openalex publication_date 2007/04/30 · arxiv created 2007/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L=5,6,7 for the square and triangular lattices. On the physical side, we obtain the exact ``phase diagrams'' for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases.