相关论文: A numerical study of the F-model with domain-wall …
We study numerically the density profile in the six-vertex model with domain wall boundary conditions. Using a Monte Carlo algorithm originally proposed by Allison and Reshetikhin we numerically evaluate the inhomogeneous density profiles…
The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…
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…
In the present article we obtain the large $N$ asymptotics of the partition function $Z_N$ of the six-vertex model with domain wall boundary conditions on the critical line between the disordered and antiferroelectric phases. Using the…
We obtain an asymptotic formula for the partition function of the six-vertex model with partial domain wall boundary conditions in the ferroelectric phase region. The proof is based on a formula for the partition function involving the…
We consider the five-vertex model on a rectangular domain of the square lattice, with the so-called `scalar-product' boundary conditions. We address the evaluation of the free-energy density of the model in the scaling limit, that is when…
We consider the homogeneous five-vertex model on a rectangle domain of the square lattice with so-called scalar-product boundary conditions. Peculiarity of these boundary conditions is that the configurations of the model are in an…
The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions…
The six-vertex F model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite-order phase transition of the Kosterlitz-Thouless type. As one of the few non-trivial exactly solved models, it…
We report on Monte-Carlo simulations of the six-vertex model with domain wall boundary conditions. In thermal equilibrium such boundary conditions force a fluctuating line separating the disordered region from the perfectly ordered ones.…
Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional $N \times N$ square lattice with the domain wall boundary conditions are considered. The one-point correlation function (`boundary polarization')…
We consider the six-vertex model with Domain Wall Boundary Conditions on a $N\times N$ square lattice. Our main interest is the study of the fluctuations of the extremal lattice path about the arctic curves. We address the problem through…
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…
In this note, we consider the six-vertex model with domain wall boundary conditions, defined on a $M\times M$ lattice, in the inhomogeneous case where the partition function depends on 2M inhomogeneities $\lambda_j$ and $\mu_k$. For a…
We study the 6-vertex model with fixed boundary conditions. In the thermodynamical limit there is a formation of the limit shape. We collect most of the known results about the analytical properties of the free energy of the model as the…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice…
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…
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,…
This is a continuation of the paper [4] of Bleher and Fokin, in which the large $n$ asymptotics is obtained for the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the disordered phase. In the…