Eight-Vertex Model in Lattice Statistics and One-Dimensional Anisotropic Heisenberg Chain

@inproceedings{Baxter1973EightVertexMI,
  title={Eight-Vertex Model in Lattice Statistics and One-Dimensional Anisotropic Heisenberg Chain},
  author={Rodney J. Baxter},
  year={1973}
}
New Developments in the Eight Vertex Model
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
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
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
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
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
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.
Scalar products of Bethe vectors in the 8-vertex model
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
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
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