Phase diagram of the chromatic polynomial on a torus

DOI10.1016/j.nuclphysb.2007.04.023zbMath1150.82006arXivcond-mat/0703228OpenAlexW2116817039WikidataQ58082404 ScholiaQ58082404MaRDI QIDQ2460850

Jesper Lykke Jacobsen, Jesús Salas

Publication date: 16 November 2007

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

Full work available at URL: https://arxiv.org/abs/cond-mat/0703228

zbMATH Keywords

conformal field theorytransfer matrixtriangular latticeantiferromagnetic Potts modelBeraha numbersFortuin-Kasteleyn representationsquare latticeChromatic polynomial

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Coloring of graphs and hypergraphs (05C15)

Related Items (13)

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings ⋮ Parallel family trees for transfer matrices in the Potts model ⋮ Transfer matrices and partition-function zeros for antiferromagnetic Potts models. V. Further results for the square-lattice chromatic polynomial ⋮ Eigenvalue amplitudes of the Potts model on a torus ⋮ Torus partition function of the six-vertex model from algebraic geometry ⋮ Phase diagram of the triangular-lattice Potts antiferromagnet ⋮ Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with extra-vertex boundary conditions ⋮ Is the five-flow conjecture almost false? ⋮ Boundary chromatic polynomial ⋮ A little statistical mechanics for the graph theorist ⋮ The three-state Potts antiferromagnet on plane quadrangulations ⋮ A generalized Beraha conjecture for non-planar graphs ⋮ Cylinder partition function of the 6-vertex model from algebraic geometry

Cites Work

• Complex-temperature phase diagram of Potts and RSOS models
• Character decomposition of Potts model partition functions. I: Cyclic geometry
• Eigenvalue amplitudes of the Potts model on a torus
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. III: Triangular-lattice chromatic polynomial
• Recursively constructible families of graphs
• \(T=0\) partition functions for Potts antiferromagnets on lattice strips with fully periodic boundary conditions
• Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. IV. Chromatic polynomial with cyclic boundary conditions
• Recursive families of graphs
• Spanning forests and the \(q\)-state Potts model in the limit \(q \to 0\)
• Chromatic polynomials of large triangular lattices
• Chromatic, Flow and Reliability Polynomials: The Complexity of their Coefficients
• Chromatic Roots are Dense in the Whole Complex Plane
• SOLUTION OF THE HEAWOOD MAP-COLORING PROBLEM
• Exact Potts model partition functions on wider arbitrary-length strips of the square lattice
• Ground state entropy of the Potts antiferromagnet on triangular lattice strips.
• 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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