The six and eight-vertex models revisited

Abstract

Elliott Lieb's ice-type models opened up the whole field of solvable models in statistical mechanics. Here we discuss the ``commuting transfer matrix'' $T,Q$ equations for these models, writing them in a more explicit and transparent notation that we believe offers new insights. The approach manifests the relationship between the six-vertex and chiral Potts models, and between the eight-vertex and Kashiwara-Miwa models.

30 pages, 6 figures

References in corpus (2)

• Completeness of the Bethe ansatz for the six and eight-vertex models
• Completing Bethe's equations at roots of unity

Cited by in corpus (22)

• Spin-1/2 XYZ model revisit: general solutions via off-diagonal Bethe ansatz
• Transfer matrix functional relations for the generalized tau_2(t_q) model
• $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms
• Universal R-matrix and functional relations
• The 8-vertex model with quasi-periodic boundary conditions
• On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra
• Quantum groups and functional relations for higher rank
• Fusion Operators in the Generalized ${\tau }^{(2)}$-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
• Bethe roots and refined enumeration of alternating-sign matrices
• The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
• The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of $U_q(s{l}_2)$
• Bazhanov-Stroganov model from 3D approach
• Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
• Solving Baxter's TQ-equation via representation theory
• On ${\tau }^{(2)}$-model in Chiral Potts Model and Cyclic Representation of Quantum Group $U_q(s{l}_2)$
• Chiral Potts Rapidity Curve Descended from Six-vertex Model and Symmetry Group of Rapidities
• On $Q$-operators of XXZ Spin Chain of Higher Spin
• Exact Results for the Residual Entropy of Ice Hexagonal Monolayer
• Free-fermion models and the two-dimensional Ising models under the zero field and imaginary field $i(\pi /2)k_{B}T$
• On the Degenerate Multiplicity of the $s{l}_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
• Quantum affine algebras and universal functional relations
• New Planar P-time Computable Six-Vertex Models and a Complete Complexity Classification