Related papers: The BCC lattice in a long range interaction system

The Standard Model while successful in many ways is incomplete; many questions remain. The origin of quark masses and hadronization of quarks are awaiting an answer. From the Dirac sea concept, we infer that two kinds of elementary quarks…

A monomer-dimer model with a short-range attractive interaction favoring colinear dimers is considered on the lattice $\mathbb{Z}^2$. Although our choice of the chemical potentials results in more horizontal than vertical dimers, the…

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…

Alkaline-earth-metal atoms exhibit long-range dipolar interactions, which are generated via the coherent exchange of photons on the 3P_0-3D_1-transition of the triplet manifold. In case of bosonic strontium, which we discuss here, this…

The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…

A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…

We consider several models of interacting bosons in a one dimensional lattice. Some of them are not integrable like the Bose-Hubbard others are integrable. At low density all of these models can be described by the Bose gas with delta…

We study a system of electrons on a one-dimensional lattice, interacting through the long range Coulomb forces, by means of a variational technique which is the strong coupling analog of the Gutzwiller approach. The problem is thus the…

The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass long-range interaction, which…

We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…

A recent paper on the large-scale structure of the Universe presented evidence for a rectangular three-dimensional lattice of galaxy superclusters and voids, with lattice spacing ~120 Mpc and called for some ``hitherto unknown process'' to…

Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…

We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…

Motivated by recent huge interests on graphene sheet and graphite as "relativistic" systems, a BCS superconductivity in a quasi-(2+1)-dimensional relativistic model is investigated. The intra-layer particle dynamics is described by a…

We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering…

We consider an ultra-small system of polarized bosons on an optical lattice with a ring topology interacting via long range dipole-dipole interactions. Dipoles polarized perpendicular to the plane of the ring reveal sharp transitions…

High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product…

Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…

A density functional theory for many-body lattice models is considered in which the single-particle density matrix is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy…

The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or…