相关论文: Exact solution of the six-vertex model with domain…

In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…

HfO$_2$- and ZrO$_2$-based ferroelectric thin films have emerged as promising candidates for the gate oxides of next generation electronic devices. Recent work has experimentally demonstrated that a tetragonal/orthorhombic (t/o-) phase…

We consider the Kinetic Fokker-Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce…

Mechanically compatible and electrically neutral domain walls in tetragonal, orthorhombic and rhombohedral ferroelectric phases of BaTiO3 are systematically investigated in the framework of the phenomenological Ginzburg-Landau-Devonshire…

Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in [15] even for symmetric convex…

Using first-principles calculations and group-theory based models, we study the stabilization of ferrielectricity (FiE) in CuInP$_2$Se$_6$. We find that the FiE ground state is stabilized by a large anharmonic coupling between the polar…

There have been a plethora of investigations carried out in studying inequalities for the Fourier coefficients of weakly holomorphic modular forms, for example, on the partition function. Recently, Bringmann, Kane, Rolen, and Tripp studied…

In this paper we consider the existence and uniqueness of pure states with some fixed slope $(s, t) \in [0, 1]^2$ for a general ferroelectric six-vertex model. First, we show there is an open subset $\mathfrak{H} \subset [0, 1]^2$, which is…

The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the…

In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large $n$ limit in the non-hermitian Penner matrix model. In these generalizations $g_n n\to t$, but…

We analyze the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory at level K. It is done in the large N, large K limits where \lambda=N/K is kept fixed. Following arXiv:1110.4386 we…

We obtain large N asymptotics for the Hermitian random matrix partition function \[Z_N(V)=\int_{\mathbb R^N}\prod_{i<j}(x_i-x_j)^2 \prod_{j=1}^N e^{-N V(x_j)}dx_j,\] in the case where the external potential $V$ is a polynomials such that…

We map out the possible ordered states in bilayer graphene at the neutrality point by extending the previous renormalization group treatment of many-body instabilities to finite temperature, trigonal warping and externally applied…

Experimental and theoretical studies of unusual polar, dielectric and magnetic properties of room temperature multiferroics, such as perovskites Pb(Fe$_{1/2}$Nb$_{1/2}$)O$_3$ (PFN) and Pb(Fe$_{1/2}$Ta$_{1/2}$)O$_3$ (PFT), are very…

We give a rigorous treatment to the thermodynamic limit of the 6-vertex model. We prove that the unique solution of the Bethe-Ansatz equation exists and the distribution of the roots converges to a continuum measure. We solve this problem…

We study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet or Neumann boundary conditions. In the case of Dirichlet boundary condition we prove…

Quantum melting of ferroelectric moment in the frustrated hydrogen-bonded system with "ice rule" is studied theoretically by using the quantum Monte Carlo simulation. The large number of nearly degenerate configurations are described as the…

We study from first-principles calculations the ferroelectric structural phase transition of Pb$_5$Ge$_3$O$_{11}$ crystal. The calculations of phonons and Born effective charges of the paraelectric phase allow us to identify a polar…

We prove sharp wavenumber-explicit error bounds for first- or second-family-N\'ed\'elec-element (a.k.a. edge-element) conforming discretisations, of arbitrary (fixed) order, of the variable-coefficient time-harmonic Maxwell equations posed…

Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain…