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Related papers: Functional relations for the six vertex model with…

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We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an…

Mathematical Physics · Physics 2009-03-11 O Foda , M Wheeler , M Zuparic

We address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model. Here we compare the bulk free energy for periodic and domain wall boundary conditions. Using a determinant representation for…

Statistical Mechanics · Physics 2009-10-31 V. Korepin , P. Zinn-Justin

Functional equations methods are a fundamental part of the theory of Exactly Solvable Models in Statistical Mechanics and they are intimately connected with Baxter's concept of commuting transfer matrices. This concept has culminated in the…

Mathematical Physics · Physics 2015-06-18 W. Galleas

In this letter we show the partition function of the 8VSOS model with domain-wall boundaries satisfies the same type of functional equations as its six-vertex model counterpart. We then use these refined functional equations to obtain novel…

Mathematical Physics · Physics 2019-02-13 W. Galleas

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions. For free-fermion vertex weights the partition function can be expressed in terms of some Hankel determinant, or equivalently…

Mathematical Physics · Physics 2015-07-23 Filippo Colomo , Andrei G. Pronko

We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin for domain wall boundary conditions, we examine some modifications of these boundary…

Statistical Mechanics · Physics 2018-05-11 Ivar Lyberg , Vladimir Korepin , G. A. P. Ribeiro , Jacopo Viti

Using the dynamical Yang-Baxter algebra we derive a functional equation for the partition function of the trigonometric SOS model with domain wall boundary conditions. The solution of the equation is given in terms of a multiple contour…

Mathematical Physics · Physics 2015-06-03 W. Galleas

We compute the exact partition function of the isotropic 6-vertex model on a cylinder geometry with free boundary conditions, for lattices of intermediate size, using Bethe ansatz and algebraic geometry. We perform the computations in both…

High Energy Physics - Theory · Physics 2020-07-24 Zoltan Bajnok , Jesper Lykke Jacobsen , Yunfeng Jiang , Rafael I. Nepomechie , Yang Zhang

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of…

Mathematical Physics · Physics 2009-11-07 J. de Gier , V. Korepin

We present the expressions for the monodromy matrix elements of the six-vertex model in the F-basis for arbitrary Boltzmann weights. The results rely solely on the property of unitarity and Yang-Baxter relations, avoiding any specific…

Mathematical Physics · Physics 2015-05-28 M. J. Martins , M. Zuparic

We describe a novel Yang-Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model…

Combinatorics · Mathematics 2020-12-07 Sylvie Corteel , Andrew Gitlin , David Keating , Jeremy Meza

We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and…

Mathematical Physics · Physics 2018-05-23 Kohei Motegi

We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.

Mathematical Physics · Physics 2011-02-16 A Caradoc , O Foda , N Kitanine

We perform a numerical study of the F-model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size…

Statistical Mechanics · Physics 2017-05-17 Rick Keesman , Jules Lamers

We review the (algebraic-)functional method devised by Galleas and further developed by Galleas and the author. We first explain the method using the simplest example: the computation of the partition function for the six-vertex model with…

Mathematical Physics · Physics 2018-06-28 Jules Lamers

A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…

Mathematical Physics · Physics 2015-05-19 Kohei Motegi

We study the thermodynamic limit of the six-vertex model with domain wall boundary and reflecting end. We evaluated the partition function explicitly in special cases. We calculated the homogeneous limit of the Tsuchiya determinant formula…

Statistical Mechanics · Physics 2015-01-14 G. A. P. Ribeiro , V. E. Korepin

We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions. In pioneering works of Korepin and Izergin a determinant formula was proposed and…

Mathematical Physics · Physics 2024-06-14 Mikhail D. Minin , Andrei G. Pronko , Vitaly O. Tarasov

We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the…

Mathematical Physics · Physics 2019-08-21 I. R. Passos , G. A. P. Ribeiro

For a particular set of Boltzmann weights and a particular boundary condition for the six vertex model in statistical mechanics, we compute explicitly the partition function and show it to be equal to a factorial Schur function, giving a…

Combinatorics · Mathematics 2009-11-01 Peter J. McNamara