Related papers: Determinant formulas for the five-vertex model

This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated…

We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group $G$. When $G=SU(2)$, the statistical weight is constructed from the $15j$-symbol as well as the $6j$-symbol for recombination of…

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,…

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…

We obtain a new representation for the partition function of the six vertex model with domain wall boundaries using a functional equation recently derived by the author. This new representation is given in terms of a sum over the…

We consider the rational six-vertex model on an L-by-L lattice with domain wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition…

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 give general conditions for the existence of a Hamiltonian operator whose discrete time evolution matches the partition function of certain solvable lattice models. In particular, we examine two classes of lattice models: the classical…

Let G be a connected reductive group. To any irreducible G-variety one assigns the lattice generated by all weights of B-semiinvariant rational functions on X, where B$ is a Borel subgroup of G. This lattice is called the weight lattice of…

The monopole-dimer model is a signed variant of the monomer-dimer model which has determinantal structure. We extend the monopole-dimer model for planar graphs (Math. Phys. Anal. Geom., 2015) to Cartesian products thereof and show that the…

In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…

Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all plane partitions whose solid Young diagrams…

In this paper, we construct the Hankel determinant representation of the rational solutions for the fifth Painlev\'{e} equation through the Umemura polynomials. Our construction gives an explicit form of the Umemura polynomials $\sigma_{n}$…

In this paper, we consider polynomials orthogonal with respect to a varying perturbed Laguerre weight $e^{-n(z-\log z+t/z)}$ for $t<0$ and $z$ on certain contours in the complex plane. When the parameters $n$, $t$ and the degree $k$ are…

The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity constraint. We show that the defining equations are derived from…

We prove a stochastic homogenization result for integral functionals defined on finite partitions assuming the surface tension to be stationary and possibly ergodic. We also consider the convergence of boundary value problems when we impose…

We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal…

The Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization to compute a…

Let K be the product O(n_1) x O(n_2) x ... x O(n_r) of orthogonal groups. Let V the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of…

In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under $Sp(4)$ symmetry. We establish a set of functional relations which include a transfer matrix…