Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0903.3089 · Journal of Mathematical Physics

Partition function of the eight-vertex model with domain wall boundary condition

Wen‐Li Yang, Yao-Zhong Zhang

Published Aug 1, 2009• 14 citations
arXivHTMLPDF

Abstract

We derive the recursive relations of the partition function for the eight-vertex model on an N×N square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.

DOI
10.1063/1.3205448

Related papers

Determinant formula for the six-vertex model

Anatoli G. Izergin, D A Coker, V. E. Korepin

The partition function of a six-vertex model with domain wall boundary conditions is considered on the finite lattice. The authors show that the partition function satisfies a recursive relation. They solve the recursion relation by a determinant formula. This gives a determinant representation for the partition function. They use the Quantum Inverse Scattering Method (QISM).

Journal of Physics A Mathematical and General•Aug 21, 1992•184 citations

Functional relations for the six-vertex model with domain wall boundary conditions

W. Galléas

In this work we demonstrate that the Yang–Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six-vertex model with domain wall boundary conditions. The homogeneous limit is studied for small lattices and the properties determining the partition function are also discussed.

arXiv:1002.1623•Journal of Statistical Mechanics Theory and Experiment•Jun 3, 2010•29 citations

On the partition function of the six-vertex model with domain wall boundary conditions

Filippo Colomo, A. G. Pronko

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ‘reconstruction’ formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.

arXiv:math-ph/0309064•Journal of Physics A Mathematical and General•Jan 28, 2004•20 citations

Drinfeld twist and the domain wall partition function of the eight-vertex model

Kun Hao, Xi Chen, Kangjie Shi +1 more

With the help of the F -basis provided by the Drinfeld twist or factorising F -matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N × N square lattice with domain wall boundary condition.

Chinese Physics B•Jan 1, 2011•1 citation

ON THE TRIGONOMETRIC FELDERHOF MODEL WITH DOMAIN WALL BOUNDARY CONDITIONS

A Caradoc, Omar E. Foda, M Wheeler +1 more

Abstract. We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda τ function. Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables. In [1], Korepin introduced domain wall boundary conditions for the six vertex model on a finite square lattice, and proposed recursion relations that determine the corresponding domain wall partition function. In [2], Izergin obtained a determinant solution of Korepin’s recursion relations. At the free fermion point, the

•Jan 1, 2007•12 citations

Factorization of rational six vertex model partition functions

Kohei Motegi

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with the explicit forms of the generalized domain wall boundary partition functions by Belliard-Pimenta-Slavnov, we derive factorization formulas for partition functions under trapezoid boundary which can be viewed as a generalization of triangular boundary. We also discuss an application to emptiness formation probabilities under trapezoid boundary which admit determinant representations.

arXiv:2410.03153•Nuclear Physics B•Nov 17, 2024•0 citations
We derive the recursive relations of the partition function for the eight-vertex model on an N×N square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.
The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ‘reconstruction’ formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.
Abstract. We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda τ function. Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables. In [1], Korepin introduced domain wall boundary conditions for the six vertex model on a finite square lattice, and proposed recursion relations that determine the corresponding domain wall partition function. In [2], Izergin obtained a determinant solution of Korepin’s recursion relations. At the free fermion point, the
We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with the explicit forms of the generalized domain wall boundary partition functions by Belliard-Pimenta-Slavnov, we derive factorization formulas for partition functions under trapezoid boundary which can be viewed as a generalization of triangular boundary. We also discuss an application to emptiness formation probabilities under trapezoid boundary which admit determinant representations.