## 261 Citations

New Developments in the Eight Vertex Model

- Mathematics
- 2002

We demonstrate that the Q matrix introduced in Baxter's 1972 solution of the eight vertex model has some eigenvectors which are not eigenvectors of the spin reflection operator and conjecture a new…

The Eight Vertex Model.New results

- Physics
- 2006

Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the…

Q-Operators for Higher Spin Eight Vertex Models with an Even Number of Sites

- Mathematics
- 2015

We construct the Q-operator for generalised eight vertex models associated to higher spin representations of the Sklyanin algebra, following Baxter’s 1973 paper. As an application, we prove the sum…

THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL

- Physics
- 1979

CONTENTS Introduction § 1. Classical statistical physics on a two-dimensional lattice and quantum mechanics on a chain § 2. Connection with the inverse problem method § 3. The six-vertex model § 4.…

The eight-vertex model and Painlevé VI equation II: eigenvector results

- Mathematics
- 2010

We study a special anisotropic -model on a periodic chain of an odd length and conjecture exact expressions for certain components of the ground state eigenvectors. The results are written in terms…

THE QUANTUM METHOD OF THE INVERSE PROBLEM AND THE HEISENBERG XYZ MODEL

- Physics
- 1979

CONTENTSIntroduction § 1. Classical statistical physics on a two-dimensional lattice and quantum mechanics on a chain § 2. Connection with the inverse problem method § 3. The six-vertex model § 4.…

Quantum inverse scattering method and the diagonal-to-diagonal transfer matrix of vertex models

- Mathematics, Physics
- 1983

Scalar products of Bethe vectors in the 8-vertex model

- MathematicsJournal of High Energy Physics
- 2020

We obtain a determinant representation of normalized scalar products of on-shell and off-shell Bethe vectors in the inhomogeneous 8-vertex model. We consider the case of rational anisotropy parameter…

The sl2 Loop Algebra Symmetry of the Six-Vertex Model at Roots of Unity

- Mathematics
- 1999

We demonstrate that the six vertex model (XXZ spin chain) with Δ=(q+q-1)/2 and q2N=1 has an invariance under the loop algebra of sl2 which produces a special set of degenerate eigenvalues. For Δ=0 we…

## References

SHOWING 1-8 OF 8 REFERENCES

One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System

- Physics
- 1966

Bethe's hypothesis is proved for the ground state of a one-dimensional cyclic chain of anisotropic nearest-neighbor spin-spin interactions. The proof holds for any fixed number of down spins.

Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric

- Physics
- 1967

The Slater KDP model is solved for all temperatures and with an electric field. Above Tc the specific heat behaves lik (T−T c )−1/2 and the polarizability like (T−T c )−1. There is first-order phase…

Exact Solution of the F Model of An Antiferroelectric

- Physics
- 1967

The F model, which was originally proposed by Rys1 as an interesting statistical mechanics problem, has since2 become a meaningful model of hydrogen bonded ferroelectrics (e.g., NH4H2PO4), at least…

Table of Integrals, Series, and Products

- Mathematics
- 1943

Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special…

Residual Entropy of Square Ice

- Physics
- 1967

At low temperatures, ice has a residual entropy, presumably caused by an indeterminacy in the positions of the hydrogen atoms. While the oxygen atoms are in a regular lattice, each O-H-O bond permits…