Related papers: Functional relations for the six vertex model with…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.
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…
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…
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…
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…
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…
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…
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…