Related papers: Minimizing Lattice Energy and Hexagonal Crystalliz…

We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…

For hamiltonian lattice gauge theory, we introduce the matrix product anzats inspired from density matrix renormalization group. In this method, wavefunction of the target state is assumed to be a product of finite matrices. As a result,…

We consider random lattice triangulations of $n\times k$ rectangular regions with weight $\lambda^{|\sigma|}$ where $\lambda>0$ is a parameter and $|\sigma|$ denotes the total edge length of the triangulation. When $\lambda\in(0,1)$ and $k$…

The low-energy properties of the two-dimensional Heisenberg model with spin-$\frac{1}{2}$ on a square lattice are investigated on the basis of the local dimer order. The lattice is divided into square blocks consisting of the quartet of…

The mode III fracture problem for a hexagonal lattice is discussed and compared with square and triangular lattices.

The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…

The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a…

We show that the standard Fermi--Pasta--Ulam system, with a suitable choice for the interparticle potential, constitutes a model for glasses, and indeed an extremely simple and manageable one. Indeed, it allows one to describe the landscape…

We study ground-state orderings of particles in classical lattice-gas models of adsorption on crystal surfaces. In the considered models, the energy of adsorbed particles is a sum of two components, each one representing the energy of a…

We consider the low energy spectrum of spin-1/2 two-dimensional triangular lattice models subject to a ferromagnetic Heisenberg interaction and a three spin chiral interaction of variable strength. Initially, we consider quasi-one…

We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple…

In this research, we examine the electronic, magnetic, and lattice properties of the Fe$_4$(P$_2$O$_7$)$_3$ compound using the first principles calculations based on the density functional theory. The crystal lattice has a monoclinic…

We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice four-Fermi or Gross-Neveu model in $d+1$ space-time dimensions ($d=1,2,3$) and with $N$-component fermions. Let $\kappa>0$ be the hopping parameter, $\lambda>0$…

We study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small…

In this paper we study a perturbative approach to the problem of quantization of measures in the plane. Motivated by the fact that, as the number of points tends to infinity, hexagonal lattices are asymptotically optimal from an energetic…

Constraints on the spin-averaged $\Lambda p$ scattering length and effective range have been obtained from measurements of the $pp\to pK^+\Lambda$ reaction close to the production threshold by comparing model phase-space Dalitz plot…

We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and…

Pairing of valence electrons can lead to energy minimization of a crystal. It can be proved by use of representation of the valence electrons as plane waves in periodic potential of the crystal.

We estimate the energy cost associated with two pancake vortices colliding in a layered superconductor. It is argued that this energy sets the plastics energy scale and is the analogue of the crossing energy for vortices in the continuum…

We study the scattering lengths of charmonia (J/psi and eta_c) with light hadrons (pi, rho and N) by the quenched lattice QCD simulations on 24x24x24x48, 32x32x32x48 and 48x48x48x48 lattices with the lattice spacing a = 0.068 fm. The…