A generalized Beraha conjecture for non-planar graphs

DOI10.1016/j.nuclphysb.2013.07.012zbMath1331.82012arXiv1303.5210OpenAlexW1968716932WikidataQ58082116 ScholiaQ58082116MaRDI QIDQ5964111

Jesper Lykke Jacobsen, Jesús Salas

Publication date: 26 February 2016

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5210

zbMATH Keywords

transfer matrixPotts modelgeneralized Petersen graphsBeraha conjectureBerker-Kadanoff phasenon-planar graphs

Mathematics Subject Classification ID

Applications of graph theory (05C90) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (5)

Torus partition function of the six-vertex model from algebraic geometry ⋮ Phase diagram of the triangular-lattice Potts antiferromagnet ⋮ Is the five-flow conjecture almost false? ⋮ Planar diagrams for local invariants of graphs in surfaces ⋮ Cylinder partition function of the 6-vertex model from algebraic geometry

Uses Software

• MPSolve

Cites Work

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• Is the five-flow conjecture almost false?
• Partition algebras.
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with extra-vertex boundary conditions
• Three-dimensional 3-state Potts model revisited with new techniques
• Complex-temperature phase diagram of Potts and RSOS models
• The antiferromagnetic transition for the square-lattice Potts model
• Character decomposition of Potts model partition functions. I: Cyclic geometry
• Eigenvalue amplitudes of the Potts model on a torus
• Zeroes of chromatic polynomials: A new approach to Beraha conjecture using quantum groups
• Boundary chromatic polynomial
• Limits of chromatic zeros of some families of maps
• Is the four-color conjecture almost false?
• Every planar map is four colorable. I: Discharging
• Flow polynomials and their asymptotic limits for lattice strip graphs
• Zeros of chromatic and flow polynomials of graphs
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. III: Triangular-lattice chromatic polynomial
• Design, analysis, and implementation of a multiprecision polynomial rootfinder
• Exact Potts model partition functions for strips of the square lattice
• Exact Potts model partition functions for strips of the triangular lattice
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. V. Further results for the square-lattice chromatic polynomial
• Phase diagram of the chromatic polynomial on a torus
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. IV. Chromatic polynomial with cyclic boundary conditions
• Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions
• Chromatic polynomials of large triangular lattices
• Chromatic, Flow and Reliability Polynomials: The Complexity of their Coefficients
• A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
• Limits of zeroes of recursively defined polynomials
• On the algebraic approach to cubic lattice Potts models
• Chromatic Roots are Dense in the Whole Complex Plane
• Series studies of the Potts model: III. The 3-state model on the simple cubic lattice
• Critical manifold of the kagome-lattice Potts model
• Transfer matrix computation of critical polynomials for two-dimensional Potts models
• A theorem on tait colorings with an application to the generalized Petersen graphs
• On the Imbedding of Linear Graphs in Surfaces
• Chromatic Polynomials
• Structural properties of Potts model partition functions and chromatic polynomials for lattice strips
• Chromatic polynomials and their zeros and asymptotic limits for families of graphs
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. I: General theory and square-lattice chromatic polynomial.
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. II: Extended results for square-lattice chromatic polynomial.

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