Hysteretic dipolar and quadrupolar properties of the spin-1 Blume–Emery–Griffiths model under pair approximation

As a continuation of previously published work [A. Erdinç and M. Keskin, Int. J. Mod. Phys. B 18, 1603 (2004), doi:10.1142/S0217979204024823] the hysteretic properties of magnetization ([Formula: see text]) and quadrupolar moment ([Formula: see text] have been investigated for the spin-1 Blume–Emery–Griffiths model using pair approximation. The magnetic field ([Formula: see text]) dependence of [Formula: see text] is produced for different values of the lattice coordination number ([Formula: see text]), biquadratic interaction ([Formula: see text]) and single-ion anisotropy ([Formula: see text]). The ([Formula: see text]) loops show different and novelty properties when [Formula: see text]. We also observed the hysteresis cycles in the ([Formula: see text], ([Formula: see text] and ([Formula: see text]) planes. These curves strongly depend on biquadratic interaction [Formula: see text]. Our results are found to be in good agreement with the other theoretical findings.

Analytical ray-tracing in planetary atmospheres

Context. Ground-based astro-geodetic observations and atmospheric radio occultations are two examples of observational techniques requiring a scrutiny analysis of atmospheric refraction. In both cases, the measured changes of the observables are geometrically related to changes in the photon path through the refractive profile of the crossed medium. Therefore, having a clear knowledge of how the refractivity governs the photon path evolution is of prime importance to clearly understand observational features. Aims. We analytically performed the integration of the photon path and the light time of rays traveling across a non-spherically symmetric planetary atmosphere. Methods. Assuming that the atmospheric refraction evolves linearly with the Newtonian potential, we derived an exact solution to the equations of geometrical optics. By varying the solution’s arbitrary constants of integration, we reformulated the equation of geometrical optics into a new set of osculating equations describing the constants’ evolution following any changes in the refractive profile. We have highlighted the capabilities of the formalism, carrying out five realistic applications in which we derived analytical expressions. Finally, we assessed the accuracy by comparing the solution to results from a numerical integration of the equations of geometrical optics in the presence of a quadrupolar moment (J2). Results. Analytical expressions for the light time and the refractive bending are given with relative errors at the level of one part in 108 and one part in 105, for typical values of the refractivity and J2 at levels of 10−4 and 10−2, respectively. Conclusions. The establishment of the osculating equations for the ray propagation has two main advantages. Firstly, it provides an easy and comprehensive geometrical picture for interpreting the photon path. Secondly, it allows the analytical solving of the ray propagation in the presence of non-radial dependencies in the refractive profile.

Local tests of gravitation with Gaia observations of Solar System Objects

In this proceeding, we show how observations of Solar System Objects with Gaia can be used to test General Relativity and to constrain modified gravitational theories. The high number of Solar System objects observed and the variety of their orbital parameters associated with the impressive astrometric accuracy will allow us to perform local tests of General Relativity. In this communication, we present a preliminary sensitivity study of the Gaia observations on dynamical parameters such as the Sun quadrupolar moment and on various extensions to general relativity such as the parametrized post-Newtonian parameters, the fifth force formalism and a violation of Lorentz symmetry parametrized by the Standard-Model extension framework. We take into account the time sequences and the geometry of the observations that are particular to Gaia for its nominal mission (5 years) and for an extended mission (10 years).

Calibration of 57Fe Mössbauer constants by first principles

Ab initio periodic esimate of Mössbauer isomer shift and quadrupolar moment for iron: hybrid functional approach in a GTO basis set.

MIXED SPIN-1 AND SPIN-$\frac{3}{2}$ BLUME–CAPEL ISING FERRIMAGNETIC SYSTEM ON THE BETHE LATTICE

The mixed spin-1 and spin-[Formula: see text] Blume–Capel Ising ferrimagnetic system for the central spin with spin-1 is studied on the Bethe lattice using the exact recursion equations. The exact expressions for the magnetization, the quadrupolar moment, the Curie temperature and the free energy are found and the phase diagrams are constructed on the Bethe lattice with the coordination numbers q = 3, 4 and 6 for the various values of the single-ion anisotropy constants dA = DA/J for spin-1 and dB = DB/J for spin-[Formula: see text]. The existence of a tricritical point is investigated for different values of q and the single-ion anisotropy constants. The phase diagrams in the (kTc/J, dA) plane for the central spin are obtained for two different cases; (1) dA = dB and (2) dA is varied for selected values of dB. The results are compared with those of other approximate methods.

THERMODYNAMIC PROPERTIES OF A MIXED SPIN-1/2 AND SPIN-1 MAGNETIC SUPERLATTICE

One considers a magnetic superlattice formed by mixed spin-1/2 and spin-1 alternate monolayers of ferromagnetic materials linked ferromagnetically with one another. Each monolayer is modelled by a simple quartic lattice of spins coupled via nearest-neighbor exchange (Ising ferromagnetic) with a single-ion anisotropy D acting in the spin-1 sites. An effective-field theory that accounts for self-spin correlation is used to study the phase diagram and magnetization curves. It is found that the phase diagrams exhibit a number of interesting phenomena resulting from the dependence of the crystal field interaction. The magnetization and quadrupolar moment curves are also shown for a range of the interaction strengths and the anisotropy parameters.

Diffusion dépolarisée Rayleigh par des molécules anisotropes: calcul analytique des contributions propres, collisionnelles et croisées pour divers potentiels

In a preceding paper, a new analytical calculation of the integrated Rayleigh light scattered intensities, taking into account the permanent anisotropy in the collisionnal polarizability tensor, has been developped. The contributions of orientational pair correlation collision induced light scattering and the cross term have been evaluated in the first order dipole induced dipole approximation, at low density in the center–center polarizability scheme. In this article, from these analytical expansions, we calculate contribution values in N2, CO2, Cl2, and O2 to the scattered intensities. The intermolecular potential is represented by a two (or three)-site Lennard–Jones model without (or with) a quadrupolar moment. We show that these new analytical calculations lead to important corrections of up to 30% for the cross term in O2, and that the potential choice plays an essential role. These results are compared with experimental data and to other studies.