Exact Potts model partition function on strips of the triangular lattice

DOI10.1016/S0378-4371(00)00225-9zbMath1052.82513arXivcond-mat/0004181OpenAlexW3102228614MaRDI QIDQ1581535

Robert Shrock, Shu-Chiuan Chang

Publication date: 3 October 2000

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

Full work available at URL: https://arxiv.org/abs/cond-mat/0004181

zbMATH Keywords

partition functionspecific heatfree boundary conditionstriangular lattice stripscyclic boundary conditions\(q\)-state Potts modelMöbius longitudinal boundary conditionsTutte-Whitney polynomialsvertex strip graphs

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (34)

On zero-free regions for the anti-ferromagnetic Potts model on bounded-degree graphs ⋮ ZEROS OF THE POTTS MODEL PARTITION FUNCTION IN THE LARGE-q LIMIT ⋮ 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 ⋮ A general method for computing Tutte polynomials of self-similar graphs ⋮ Parallel family trees for transfer matrices in the Potts model ⋮ Complex-temperature phase diagram of Potts and RSOS models ⋮ Tutte polynomial of pseudofractal scale-free web ⋮ Measures of spin ordering in the Potts model with a generalized external magnetic field ⋮ Exact partition functions for the \(q\)-state Potts model with a generalized magnetic field on lattice strip graphs ⋮ The Tutte polynomial of some matroids ⋮ Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with extra-vertex boundary conditions ⋮ On the exact evaluation of certain instances of the Potts partition function by quantum computers ⋮ Tutte polynomials and related asymptotic limiting functions for recursive families of graphs ⋮ Asymptotic behavior of spanning forests and connected spanning subgraphs on two-dimensional lattices ⋮ q-plane zeros of the Potts partition function on diamond hierarchical graphs ⋮ Tutte polynomial of the Apollonian network ⋮ Exact chromatic polynomials for toroidal chains of complete graphs ⋮ EXACT PARTITION FUNCTION FOR THE POTTS MODEL WITH NEXT-NEAREST NEIGHBOR COUPLINGS ON ARBITRARY-LENGTH LADDERS ⋮ Chromatic polynomials for lattice strips with cyclic boundary conditions ⋮ Structural properties of Potts model partition functions and chromatic polynomials for lattice strips ⋮ 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 ⋮ Ground state entropy of the Potts antiferromagnet on triangular lattice strips. ⋮ Zeros of Jones polynomials for families of knots and links ⋮ Potts model partition functions for self-dual families of strip graphs ⋮ Potts model partition functions on two families of fractal lattices ⋮ Zeros of the Potts model partition function on Sierpinski graphs ⋮ Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs ⋮ DETERMINING THE COMPONENT NUMBER OF LINKS CORRESPONDING TO TRIANGULAR AND HONEYCOMB LATTICES ⋮ General structural results for Potts model partition functions on lattice strips ⋮ Ground state entropy of the Potts antiferromagnet on strips of the square lattice ⋮ Complex-\(q\) zeros of the partition function of the Potts model with long-range interactions

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