Search results for "Nearest neighbor"
showing 10 items of 63 documents
Spin and charge orderings in the atomic limit of the U-V-J model
2011
In this paper we study a generalization of the 1D Hubbard model by considering density-density and Ising-type spin-spin nearest neighbor (NN) interactions, parameterized by $V$ and $J$, respectively. We present the T=0 phase diagram for both ferro ($J>0$) and anti-ferro ($J<0$) coupling obtained in the narrow-band limit by means of an extension to zero-temperature of the transfer-matrix method. Based on the values of the Hamiltonian parameters, we identify a number of phases that involve orderings of the double occupancy, NN density and spin correlations, being these latter very fragile.
Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice
2005
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity whic…
Wetting and layering in the nearest-neighbor simple-cubic Ising lattice: A Monte Carlo investigation.
1988
Critical, tricritical, and first-order wetting transitions are studied in a simple-cubic nearest-neighbor Ising model, with exchange J in the bulk and exchange ${J}_{s}$ in the surface planes, by applying suitable bulk and surface fields H and ${H}_{1}$. Monte Carlo calculations are presented for systems of size L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D, in a thin film geometry with D=40 layers and two free L\ifmmode\times\else\texttimes\fi{}L surfaces, with L ranging from L=10 to L=50. In addition, evidence for prewetting transitions and for layering transitions (the latter occur for temperatures T less than the roughening temperature ${T}_{R}$) is presented. …
Classical Heisenberg antiferromagnets with nearest and next-nearest neighbor interactions on the face-centered cubic lattice: a model for EuTe?
1989
Magnetic properties of the Heisenberg antiferromagnet with spin quantum numberS→∞ on the face-centered cubic lattice are studied as function of temperature and magnetic field, using molecular field approximation and Monte Carlo methods. In order to model Europiumtelluride, we use isotropic exchange interactions between nearest- and nextnearest neighbors; the values of these exchange constants are taken from experiments. In addition, a pseudo-dipolar anisotropy (truncated after the next-nearest neighbor distance) is included; the molecular field calculations also are performed with the full dipolar of real EuTe in two respects: the structure in zero magnetic field involves 8 sublattices in t…
Modulational stability brought by cubic–quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential
2022
Abstract This work extends to higher-order interactions the results of Ref. Nguetcho (2021), in which we discussed only on modulational instability in one-dimensional chain made of atoms, harmonically coupled to their nearest neighbors and subjected to an external on-site potential. Here we investigate the competition between cubic-quartic nonlinearities interactions of the nearest-neighbor and substrate’s deformability, and mainly discuss its impact on the modulational instability of the system. This makes it possible to adapt the theoretical model to a real physical system such as atomic chains or DNA lattices. The governing equation, derived from the modified Frenkel-Kontorova model, is …
Phase Transitions in Multicomponent Widom-Rowlinson Models
1995
We use Monte Carlo techniques to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. For M between two and six there is a direct transition from the gas phase at z z d (M). For M ≥ 7 there is an intermediate ordered phase in which the even (or odd) sublattice is occupied preferentially by particles chosen at random from any of the species. The existence of such an intermediate phase was proven earlier for M ≥ M 0, M 0 very large. Exact calculations on the Bethe lattice give M0 = 4.
The Ising square lattice in aL�M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers
1989
Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthM≫L, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a “terrace” of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary “fields” is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the …
Monte Carlo simulation of phase separation and clustering in the ABV model
1991
As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump ratesΓ A andΓ B, respectively. For a small concentration of vacancies (c v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk 1(t),k 2 2 (t) is studied during the early stages of phase separation, for several choices of co…
Finite-Size Scaling Study of the Simple Cubic Three-State Potts Glass
1991
During the last few years the Potts glass model has attracted more and more attention. It is considered as a first step towards modelling the phase transition of structural and orientational glasses. A mean-field approach /1/ predicts a low temperature behavior completely different from what is known from Ising spin glasses /2/. But short range models differ markedly from mean-field-predictions. So it is natural to ask, how the short range Potts glass behaves. Especially the question of the lower critical dimension d l is important, below which a finite temperature transition ceases to occur. We tried to answer this by combining Monte-Carlo simulations with a finite-size scaling analysis. T…
Multiparticle breathers for a chain with double-quadratic on-site potential
1999
We investigate the existence and properties of multiparticle breathers for a one-dimensional model with harmonic nearest neighbor interactions where a group of r particles $(r=1,2,3,\dots{})$ perform interwell oscillations between both wells of a double-quadratic on-site potiential. We find two types of such breathers. For the first type the breather frequency $\ensuremath{\Omega}$ is within the single-particle oscillator spectrum, and the ``residence'' time of each breather particle in the left and right well is about the same. For the second breather $\ensuremath{\Omega}$ is below that spectrum, and the ratio ${\ensuremath{\tau}}_{L}/{\ensuremath{\tau}}_{R}$ of the residence time in the l…