相关论文: Exact solution of the six-vertex model with domain…
We consider Bridgeland stability conditions for three-folds conjectured by Bayer-Macr\`i-Toda in the case of Picard rank one. We study the differential geometry of numerical walls, characterizing when they are bounded, discussing possible…
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 carry out the asymptotic analysis as $n \to \infty$ of a class of orthogonal polynomials $p_{n}(z)$ of degree $n$, defined with respect to the planar measure \begin{equation*} d\mu(z) = (1-|z|^{2})^{\alpha-1}|z-x|^{\gamma}\mathbf{1}_{|z|…
We consider a two-dimensional point process whose points are separated into two disjoint components by a hard wall, and study the multivariate moment generating function of the corresponding disk counting statistics. We investigate the…
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…
The physics of ferroelectric domain walls is explored using the Bayesian inference analysis of atomically resolved STEM data. We demonstrate that domain wall profile shapes are ultimately sensitive to the nature of the order parameter in…
Using first-principles calculations, we predict that tunable ferroelectricity can be realized in oxide perovskites with the Grenier structure and ordered oxygen vacancies. Specifically, we show that $R_{1/3}A_{2/3}\mathrm{FeO}_{2.67}$…
We study the asymptotics of large, simple, labeled graphs constrained by the densities of edges and of $k$-star subgraphs, $k\ge 2$ fixed. We prove that under such constraints graphs are "multipodal": asymptotically in the number of…
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…
Domain structure of a fluid ferroelectric nematic is dramatically different from the domain structure of solid ferroelectrics since it is not restricted by rectilinear crystallographic axes and planar surface facets. We demonstrate that…
Phase-field simulation (PFS) have revolutionized the understanding of domain structure and switching behavior in ferroelectric thin films and ceramics. Generally, PFS is based on solution of a (set) of Ginzburg-Landau equations for a…
Let $f \in \mathbb{Z}[y]$ be a polynomial such that $f(\mathbb{N}) \subseteq \mathbb{N}$, and let $p_{\mathcal{A}_{f}}(n)$ denote number of partitions of $n$ whose parts lie in the set $\mathcal{A}_f:=\{f(n):n \in \mathbb{N}\}$. Under…
For Sn$_2$P$_2$S$_6$ ferroelectrics, the appearance of spontaneous polarization is related to stereoactivity of tin cations and valence fluctuations of phosphorous cations. Here, the continuous phase transition and its behavior under…
Analytical description of domain structure morphology and phase diagrams of ferroelectric nanoparticles is developed in the framework of Landau Ginzburg Devonshire approach. To model realistic conditions of incomplete screening of…
For a function g(w) analytic and univalent in {w:1<|w|<\infty} with a simple pole at \infty and a continuous extension to {w:|w|\geq 1}, we consider the Faber polynomials F_n(z), n=0,1,2,..., associated to g(w) via their generating function…
The structure of 180-degree uncharged rotational domain wall in a multiaxial ferroelectric film is studied within the framework of analytical Landau-Ginzburg-Devonshire (LGD) approach. The Finite Element Modelling (FEM) is used to solve…
We exhibit some large variations solutions of the Landau-Lifschitz equations as the exchange coefficient ε^2 tends to zero. These solutions are described by some asymptotic expansions which involve some internals layers by means of…
We study the behavior of configurations in the symmetric six-vertex model with $a,b,c$ weights in the $n\times n$ square with Domain Wall Boundary Conditions as $n\to\infty$. We prove that when $\Delta=\frac{a^2+b^2-c^2}{2ab}<1$,…
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…
Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in $\mathcal{L}\subset\mathbb{N}$ ($\gcd(\mathcal{L})=1$) and good analytic properties of the corresponding zeta function, generalizing work…