Related papers: A note on a boundary one point function for the si…
In this work we elaborate on a previous result relating the partition function of the six-vertex model with domain-wall boundary conditions to eigenvalues of a transfer matrix. More precisely, we express the aforementioned partition…
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…
Fundamental properties of spontaneous and piezo polarization are reformulated and critically reviewed. It was demonstrated that Landau definition of polarization as a dipole density could be used to the infinite systems. The difference…
We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in…
We analyze the paraxial beam transformation upon reflection and refraction at a plane boundary. In contrast to the usual approach dealing with the beam angular spectrum, we apply the continuity conditions to explicit spatial representations…
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…
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…
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…
We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…
We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy…
Belavin's $\mathbb{Z}_n$-symmetric elliptic model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We find non-diagonal $K$-matrices for $n>2$ that satisfy the reflection equation (boundary Yang--Baxter…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
In this letter, the 6-vertex model on dynamical random lattices is defined via a matrix model and rewritten (following I. Kostov) as a deformation of the O(2) model. In the large N planar limit, an exact solution is found at criticality.…
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.
(i) Uncountably many synchronized reflected Brownian motions can hit the boundary of a $C^2$ domain at the same time. (ii) Measures associated to local times of two synchronized reflected Brownian motions are mutually singular until the…
The normalisation relation between the bound and scattering S-state wave functions, extrapolated to the bound state pole, is derived from the Schroedinger equation. It is shown that, unlike previous work, the result does not depend on the…
To assess the strength of nematic fluctuations with a finite wave vector in a two-dimensional metal, we compute the static d-wave polarization function for tight-binding electrons on a square lattice. At Van Hove filling and zero…
We derived the corresponding boundary condition on Fermi fields to the spin-1/2 Heisenberg chain with boundary magnetic fields. In order to obtain the correct boundary condition from the variation of the action at the edges, we carefully…
The term "surface polarization" is introduced to describe the in-plane polarization existing at the surface of an insulating crystal when the in-plane surface inversion symmetry is broken. Here, the surface polarization is formulated in…