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:1411.2903

The domain wall partition function for the Izergin-Korepin 19-vertex model at a root of unity

Alexandr Garbali

Published Nov 11, 2014• 3 citations
arXivHTMLPDF

Abstract

We study the domain wall partition function $Z_N$ for the $U_q(A_2^{(2)})$ (Izergin-Korepin) integrable $19$-vertex model on a square lattice of size $N$. $Z_N$ is a symmetric function of two sets of parameters: horizontal $ζ_1,..,ζ_N$ and vertical $z_1,..,z_N$ rapidities. For generic values of the parameter $q$ we derive the recurrence relation for the domain wall partition function relating $Z_{N+1}$ to $P_N Z_N$, where $P_N$ is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables $ζ_1,..,ζ_N$ and $z_1,..,z_N$. After setting $q^3=-1$ the recurrence relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by $P_N$.

DOI
10.48550/arxiv.1411.2903

Related papers

The domain wall partition function for the Izergin–Korepin nineteen-vertex model at a root of unity

Alexandr Garbali

Abstract We study the domain wall partition function Z N for the (Izergin–Korepin) integrable nineteen-vertex model on a square lattice of size N . Z N is a symmetric function of two sets of parameters: horizontal and vertical rapidities. For generic values of the parameter q we derive the recurrence relation for the domain wall partition function relating Z N +1 to , where P N is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables and . After setting the recurrence relation simplifies and we solve it in terms of a Jacobi–Trudi-like determinant of polynomials generated by P N .

Journal of Statistical Mechanics Theory and Experiment•Mar 1, 2016•4 citations

Izergin-Korepin approach to symmetric functions

Kohei Motegi, Kazumitsu Sakai

Recently, the Izergin-Korepin technique, which was originally a method to the analyze the domain wall boundary partition functions initiated by Korepin and Izergin, was extended to the wavefunctions of integrable six-vertex models. We illustrate for the case of the rational integrable models.

Journal of Physics Conference Series•Apr 1, 2019•0 citations

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

Domain wall boundary partition function of the six-vertex model with triangular boundary

Kohei Motegi

We introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the $U_q(sl_2)$ $R$-matrix and a special class of the triangular $K$-matrix. By using its graphical representation, we make the Izergin-Korepin analysis with the help of the Yang-Baxter relation and the reflection equation to give a characterization of the partition function. The explict form of the symmetric function representing the partition function is presented by showing that it satisfies all the required properties.

arXiv:1703.06250•Mar 18, 2017•1 citation

Functional relations in nineteen-vertex models with domain-wall boundaries

A. Bossart, W. Galléas

This work is concerned with functional properties shared by partition functions of nineteen-vertex models with domain-wall boundary conditions. In particular, we describe both Izergin-Korepin and Fateev-Zamolodchikov models with the aforementioned boundary conditions and show that their partition functions are governed by a system of functional equations originating from the associated Yang-Baxter algebra.

arXiv:1810.06482•Journal of Mathematical Physics•Oct 1, 2019•5 citations

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

Wen‐Li Yang, Yao-Zhong Zhang

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.

arXiv:0903.3089•Journal of Mathematical Physics•Aug 1, 2009•14 citations
We study the domain wall partition function ZNZ_NZN​ for the Uq(A2(2))U_q(A_2^{(2)})Uq​(A2(2)​) (Izergin-Korepin) integrable 191919-vertex model on a square lattice of size NNN. ZNZ_NZN​ is a symmetric function of two sets of parameters: horizontal ζ1,..,ζNζ_1,..,ζ_Nζ1​,..,ζN​ and vertical z1,..,zNz_1,..,z_Nz1​,..,zN​ rapidities. For generic values of the parameter qqq we derive the recurrence relation for the domain wall partition function relating ZN+1Z_{N+1}ZN+1​ to PNZNP_N Z_NPN​ZN​, where PNP_NPN​ is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables ζ1,..,ζNζ_1,..,ζ_Nζ1​,..,ζN​ and z1,..,zNz_1,..,z_Nz1​,..,zN​. After setting q3=−1q^3=-1q3=−1 the recurrence relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by PNP_NPN​.
Abstract We study the domain wall partition function Z N for the (Izergin–Korepin) integrable nineteen-vertex model on a square lattice of size N . Z N is a symmetric function of two sets of parameters: horizontal and vertical rapidities. For generic values of the parameter q we derive the recurrence relation for the domain wall partition function relating Z N +1 to , where P N is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables and . After setting the recurrence relation simplifies and we solve it in terms of a Jacobi–Trudi-like determinant of polynomials generated by P N .
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 introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the Uq(sl2)U_q(sl_2)Uq​(sl2​) RRR-matrix and a special class of the triangular KKK-matrix. By using its graphical representation, we make the Izergin-Korepin analysis with the help of the Yang-Baxter relation and the reflection equation to give a characterization of the partition function. The explict form of the symmetric function representing the partition function is presented by showing that it satisfies all the required properties.