Two-sublattice Ising Model Research Articles

Critical behavior of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H) and transverse (Ω) fields by using the effective-field theory. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction in the presence of the H and Ω fields. We obtain the phase diagrams in the H–T and Ω–T planes changing values of the Ω and H parameters, respectively for fixed value at λ=Jx/Jy=1. At null temperature, the ground state phase diagram in the Ω–H plane for several values of λ parameter is analyzed. In the particular case of λ=1 we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field Hc/Jy=2.0 for Ω=0 by using EFT.

The decorated ferrimagnetic Ising model in a transverse field

The effect of a transverse field on the magnetizations and phase diagrams of a decorated two-sublattice Ising model ferrimagnetic consisting of two magnetic atoms A and B with spins A = 1/2 and SB = 1 is investigated within the framework of the effective field theory. A number of characteristic phenomena, such as the possibility of compensation points and two transitions, are found.

Mean-field Green's-function theory of the two-sublattice Ising model in a transverse field.

Double-time Green's functions are used within a mean-field treatment of the two-sublattice Ising model in a transverse field. In contrast to previous treatments, a correct version of the spectral theorem is used to obtain a correct mean-field treatment for all spin. In particular, the dielectric constant is obtained for S=1. The results are markedly different from those of earlier treatments and are readily extended to four-sublattice models.

An extended version of Gaussian fluctuations approximation. Application for an Ising model with positive biquadratic interaction

Summing up a certain infinite class of diagrams for the Ising model (S = 1) with biquadratic interaction, the authors have obtained an extended version of the Gaussian fluctuation approximation which takes into account both molecular and quadrupolar fields fluctuations. The resulting self-consistent equations allow us to determine order parameters as well as free energy which satisfies stationary conditions. With the use of this method, the two-sublattice Ising model with positive biquadratic term and single-ion anisotropy is investigated. The obtain results, which in the limit T → 0 contradict the predictions of the molecular field approximation, seem to be in agreement with Monte Carlo simulations and other methods.

Antiferrodistortive structural phase transition in the Jahn-Teller system DyKMo2O8. I. Raman scattering and infrared absorption studies

A cooperative Jahn-Teller effect is observed in the orthorhombic layered rare-earth compound DyKMo2O8 at TD=14.3 K. Raman and infrared spectra show a mode near 30 cm-1 at 2 K which decreases in energy in a mean-field fashion with increasing temperature up to TD. The Raman spectra show also a well defined mode at approximately 22 cm-1 which becomes overdamped at 10 K and whose intensity decreases continuously to zero at TD. This soft mode is neither Raman or infrared active above TD. Estimates of the ion-lattice coupling show that a B-symmetry local distortion is favoured, and a comparison of the spectroscopic data with group theoretical predictions suggest that the transition is antiferrodistortive. A two-sublattice Ising model which includes intra- and inter-sublattice effective exchange interactions, J(k) and H(k), is developed and is found to display the two-mode behaviour observed: the lower-energy soft mode follows the order parameter (Sz) whereas the upper mode has the energy of the mean field. A fit to the Raman data yields the result J(0) approximately=H(0)=7.5 cm-1.

Dipol-octopol interaction spin model for temperature-induced metamagnets

A two-sublattice Ising model is proposed with special dipol-octopol interaction. This special interaction term is not the even function of the spin sublattice operators. Thermodynamical properties of this model are investigated in the molecular field approximation. Our results agree satisfactory with experimental data for Mn 3GaC.

Spin-lattice coupling and tricritical behavior in the FeCl 2 metamagnet

A two-sublattice Ising model is employed to determine the phase boundary of the FeCl 2 metamagnet for every value of the external pressure. An effective spin hamiltonian is obtained in the λ-ensemble and the competing ferro- and antiferromagnetic exchange interactions depend on external pressure. The Néel temperature and the tricritical point are explicitly determined as a function of pressure in the low and high pressure regions of FeCl 2. We show that the change in the signal of the slope of the line of tricritical points with pressure may be ascribed to the change in the ferromagnetic spin-lattice coupling.

Phase boundary of a compressible metamagnetic model

A two-sublattice Ising model is considered to study the phase boundary of a compressible metamagnetic model. An effective spin Hamiltonian is obtained in the lambda -ensemble where the competing ferro- and antiferromagnetic exchange interactions depend on external force. Through Bogoliubov's inequality and Landau's theory of the continuous phase transitions the authors determined the phase boundary in the magnetic field-temperature plane for several values of the external force lambda . The Neel temperature and the tricritical point are explicitly determined as a function of this force. They also show that the tricritical behaviour disappears above a given value of the external force.

Dynamics of the two-sublattice Ising model in a transverse field studied using a coupled-operators continued-fraction expansion

The dynamics of the longitudinal spin fluctuations of the two-sublattice three-dimensional Ising model in a transverse field is studied using a continued-fraction expansion for coupled operators.

Isotope effects in Rochelle salt

Isotope effects on deuteration both in the static and dynamical behaviour of Rochelle salt are theoretically investigated on the basis of a two-sublattice Ising model with asymmetric double-well potential. Spontaneous polarization and static dielectric constant are numerically calculated for several values of the tunnelling integral. The dynamical susceptibility is derived from a Bloch-type equation, and the shifts of the relaxation times are calculated from this equation. The notable difference in the dynamical behaviour between Rochelle salt and KDP-type ferroelectrics is also discussed.

A simple model describing all types of collinear metamagnets

Abstract A two-sublattice Ising model is proposed with four-spin interactions added for the description of all types of collinear metamagnets.