Sum Rule for the Eight-Vertex Model on Its Combinatorial Line

DOI10.1007/978-1-4471-4863-0_26zbMath1272.82012arXiv1202.4420OpenAlexW1512591697MaRDI QIDQ2842073

Paul Zinn-Justin

Publication date: 31 July 2013

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.4420

zbMATH Keywords

XYZ spin chaineight-vertex modelinhomogeneous transfer matrix

Mathematics Subject Classification ID

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

Related Items

A combinatorial description of certain polynomials related to the XYZ spin chain. II: The polynomials \(p_n\) ⋮ Nearest-neighbour correlation functions for the supersymmetric XYZ spin chain and Painlevé VI ⋮ Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions ⋮ Spin chains with dynamical lattice supersymmetry ⋮ On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions ⋮ A combinatorial description of certain polynomials related to the XYZ spin chain ⋮ The nineteen-vertex model and alternating sign matrices ⋮ Elliptic pfaffians and solvable lattice models ⋮ Multivariate quadratic transformations and the interpolation kernel ⋮ On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions ⋮ Special polynomials related to the supersymmetric eight-vertex model: a summary ⋮ Sum rules for the supersymmetric eight-vertex model ⋮ Koornwinder polynomials and the \(XXZ\) spin chain ⋮ Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder