Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models III. Triangular-Lattice Chromatic Polynomial

Abstract

We study the chromatic polynomial P_G(q) for m \times n triangular-lattice strips of widths m <= 12_P, 9_F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin--Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m,n\to\infty and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.

105 pages, LaTeX2e. Self-unpacking archive containing the tex file, three sty files, 36 ps files, and a Mathematica file (transfer3.m). The background material can be found in cond-mat/0004330 and cond-mat/0011456. Section 6 has been rewritten and new results are presented. To be published in J. Stat. Phys

References in corpus (3)

• Exact Potts Model Partition Function for Strips of the Square Lattice
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
• General Structural Results for Potts Model Partition Functions on Lattice Strips

Cited by in corpus (24)

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• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions
• A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm
• Complex-temperature phase diagram of Potts and RSOS models
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
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• Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices
• 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
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• Phase diagram of the triangular-lattice Potts antiferromagnet
• What is the probability of connecting two points ?
• A generalized Beraha conjecture for non-planar graphs
• A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
• 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
• Critical Behaviour of Spanning Forests on Random Planar Graphs
• From hard spheres to hard-core spins
• Parallel family trees for transfer matrices in the Potts model
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs