Structural properties of Potts model partition functions and chromatic polynomials for lattice strips

DOI10.1016/S0378-4371(01)00150-9zbMath0978.82023arXivcond-mat/0005232OpenAlexW2029936840MaRDI QIDQ5936863

Robert Shrock, Shu-Chiuan Chang

Publication date: 9 July 2001

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0005232

zbMATH Keywords

Catalan numberChebyshev polynomial of the second kindchromatic polynomialcoloring methodsdirected lattice animalsMotzkin numberPotts model partition functionstemperature dependent variabletransfer matrix methodsTutte polynomial

Mathematics Subject Classification ID

Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Coloring of graphs and hypergraphs (05C15)

Related Items (18)

PARTITION FUNCTION ZEROS OF A RESTRICTED POTTS MODEL ON SELF-DUAL STRIPS OF THE SQUARE LATTICE ⋮ Structure of the partition function and transfer matrices for the Potts model in a magnetic field on lattice strips ⋮ Transfer matrices and partition-function zeros for antiferromagnetic Potts models. V. Further results for the square-lattice chromatic polynomial ⋮ Tutte polynomials of bracelets ⋮ Complex-temperature phase diagram of Potts and RSOS models ⋮ Algebraic methods for chromatic polynomials. ⋮ Tutte polynomials and related asymptotic limiting functions for recursive families of graphs ⋮ Weighted graph colorings ⋮ Exact Potts model partition functions for strips of the honeycomb lattice ⋮ Weighted-set graph colorings ⋮ Exact chromatic polynomials for toroidal chains of complete graphs ⋮ Chromatic polynomials for lattice strips with cyclic boundary conditions ⋮ Exact Potts model partition functions on strips of the honeycomb lattice ⋮ Exact Potts model partition functions on wider arbitrary-length strips of the square lattice ⋮ A little statistical mechanics for the graph theorist ⋮ Potts model partition functions for self-dual families of strip graphs ⋮ A generalized Beraha conjecture for non-planar graphs ⋮ General structural results for Potts model partition functions on lattice strips

Uses Software

• OEIS

Cites Work

• Limits of chromatic zeros of some families of maps
• Is the four-color conjecture almost false?
• Catalan, Motzkin, and Riordan numbers
• The coloring of graphs
• New enumerative results on two-dimensional directed animals
• Exact Potts model partition function on strips of the triangular lattice
• Spanning trees on hypercubic lattices and nonorientable surfaces
• Ground state entropy of the Potts antiferromagnet on strips of the square lattice
• Approximations for chromatic polynomials
• A connection between complex-temperature properties of the \(1\)D and \(2\)D spin \(s\) Ising model
• \(T=0\) partition functions for Potts antiferromagnets on Möbius strips and effects of graph topology
• Recursive families of graphs
• Coefficients of chromatic polynomials
• Chromatic polynomials of large triangular lattices
• Equivalence of the Potts model or Whitney polynomial with an ice-type model
• Spanning trees on graphs and lattices inddimensions
• Extension of the Kasteleyn-Fortuin formulas to directed percolation
• Solvability of Some Statistical Mechanical Systems
• Ground state entropy of Potts antiferromagnets on cyclic polygon chain graphs
• On dichromatic polynomials
• Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products
• A Contribution to the Theory of Chromatic Polynomials
• Motzkin numbers
• A new 5‐arc‐transitive cubic graph
• Motzkin numbers
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