Related papers: Emptiness formation probability in the domain-wall…
In the six-vertex model with domain wall boundary conditions, the emptiness formation probability is the probability that a rectangular region in the top left corner of the lattice is frozen. We generalize this notion to the case where the…
We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…
We show that the emptiness formation probability of the six-vertex model with domain wall boundary conditions at its free-fermion point is a $\tau$-function of the sixth Painlev\'e equation. Using this fact we derive asymptotics of the…
The problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions is addressed by considering a particular nonlocal correlation function, called row configuration probability. This correlation…
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…
The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this…
We study the emptiness formation probability, along with various representations for nonlocal correlation functions, of the 20-vertex model. In doing so, we leverage previous arguments for representations of nonlocal correlation functions…
Correlation functions of the six and nineteen vertex models on an N \times N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by use…
The problem of the limit shape of large alternating sign matrices (ASMs) is addressed by studying the emptiness formation probability (EFP) in the domain-wall six-vertex model. Assuming that the limit shape arises in correspondence to the…
We define a new family of overlaps $C_{N,m}$ for the XXZ Hamiltonian on a periodic chain of length $N$. These are equal to the linear sums of the groundstate components, in the canonical basis, wherein $m$ consecutive spins are fixed to the…
We study the relationship between various integral formulas for nonlocal correlation functions of the six-vertex model with domain wall boundary conditions. Specifically, we show how the known representation for the emptiness formation…
We summarize how to obtain rough bounds for one version of the emptiness formation probability in the 2d dimer model. The methods we use are the same as have been developed to obtain EFP bounds in the 1d XXZ model in a paper with Crawford,…
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…
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…
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 consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
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…
In this work we demonstrate that the Yang-Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six vertex model with domain wall boundary conditions. The homogeneous limit is studied…
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…