Related papers: Elliptic dynamical reflection algebra and partitio…
In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an…
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a…
With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we obtain the explicit determinant expression of the partition function of the eight-vertex model with a generic non-diagonal reflecting end and…
In this work we refine the method of [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation is originated from the dynamical…
In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional…
We generalize a recent observation [arXiv:math/0610433] that the partition function of the 6-vertex model with domain-wall boundary conditions can be obtained by computing the projections of the product of the total currents in the quantum…
In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall…
With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model…
A Potts model with a reflecting boundary is introduced and it is shown that its partition function can be expressed as a Markov trace on the Temperley-Lieb Algebra of Coxeter type B.
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 $U_q(sl_2)$…
We extend the recently developed Izergin-Korepin analysis on the wavefunctions of the $U_q(sl_2)$ six-vertex model to the reflecting boundary conditions. Based on the Izergin-Korepin analysis, we determine the exact forms of the symmetric…
We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin-Korepin formula for the six-vertex model. As applications, we find…
In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid…
The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is considered. The partition function is computed using the Izergin-Korepin method,…
In this article, we study elliptic stochastic partial differential equations with two reflect- ing walls h1 and h2, driven by multiplicative noise. The existence and uniqueness of the solutions are established.
We obtain a diagonal solution of the dual reflection equation for elliptic $A^{(1)}_{n-1}$ SOS model. The isomorphism between the solutions of the reflection equation and its dual is studied.
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…
We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with the homogeneous Dirichlet…
We prove a duality formula between two elliptic determinants. We present a proof which is a variant of the Izergin-Korepin method which is a method originally introduced to analyze and compute partition functions of integrable lattice…
In this work we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group $\mathcal{E}_{p, \gamma}[\widehat{\mathfrak{gl}_2}]$ as its underlying symmetry algebra. We elaborate on results previously…