Phase diagram of the chromatic polynomial on a torus
arXiv:cond-mat/0703228 · doi:10.1016/j.nuclphysb.2007.04.023
Abstract
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.
arXiv comment72 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
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- Transfer matrix computation of critical polynomials for two-dimensional Potts models
- Critical points in coupled Potts models and critical phases in coupled loop models
- A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm
- Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
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- Is the five-flow conjecture almost false?
- Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices
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- Phase diagram of the triangular-lattice Potts antiferromagnet
- 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
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- The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
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- Bootstrap approach to geometrical four-point functions in the two-dimensional critical -state Potts model: A study of the -channel spectra
- Potts critical frontiers of inhomogeneous and asymmetric bow-tie lattices
- Parallel family trees for transfer matrices in the Potts model
- Torus partition function of the six-vertex model from algebraic geometry