Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models II. Extended Results for Square-Lattice Chromatic Polynomial

Abstract

We study the chromatic polynomials for m \times n square-lattice strips, of width 9 <= m <= 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n \to \infty. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.

22 pages, LaTeX2e. Source includes Mathematica file transfer2.m. The background material can be found in cond-mat/0004330. Final version with many changes in Section 4

References in corpus (5)

• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• T=0 Partition Functions for Potts Antiferromagnets on Square Lattice Strips with (Twisted) Periodic Boundary Conditions
• Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice
• T=0 Partition Functions for Potts Antiferromagnets on Lattice Strips with Fully Periodic Boundary Conditions
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

Cited by in corpus (26)

• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Spanning forests and the q-state Potts model in the limit q \to 0
• A Little Statistical Mechanics for the Graph Theorist
• Counting colored planar maps: algebraicity results
• Phase diagram of the chromatic polynomial on a torus
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models III. Triangular-Lattice Chromatic Polynomial
• $q$-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
• Q-colourings of the triangular lattice: Exact exponents and conformal field theory
• Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices
• The three-state Potts antiferromagnet on plane quadrangulations
• Transfer Matrices for the Partition Function of the Potts Model on Toroidal Lattice Strips
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
• General Structural Results for Potts Model Partition Functions on Lattice Strips
• Phase diagram of the triangular-lattice Potts antiferromagnet
• Potts model on recursive lattices: some new exact results
• A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
• A generalized Beraha conjecture for non-planar graphs
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips
• Integrability vs non-integrability: Hard hexagons and hard squares compared
• Exact Chromatic Polynomials for Toroidal Chains of Complete Graphs
• Parallel family trees for transfer matrices in the Potts model
• Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions
• Exact Potts/Tutte Polynomials for Hammock Chain Graphs