Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Critical temperatures for a spin-1 Ising model with dipolar and quadrupolar interactions

Aline Franco Siqueira, I. P. Fittipaldi

Published May 1, 1985• 36 citations
Publisher

Abstract

The critical temperature for an isotropic Blume-Emery-Griffiths model is discussed in a new type of effective-field approximation. The method, which can systematically include correlation effects, is illustrated by applying to a linear, honeycomb, and simple-cubic lattices. The relation between the present method and that very recently proposed by Chakraborty is widely discussed.

DOI
10.1103/physrevb.31.6092

Related papers

The dilute spin-one Ising model on a honeycomb lattice

Viktor Urumov

Given some restriction on the interaction parameters, the critical temperature for the spin-one Ising model on a honeycomb lattice described with the Blume-Emery-Griffiths Hamiltonian with random non-magnetic impurities in equilibrium (annealed site-disorder case) is obtained exactly.

Journal of Physics Condensed Matter•Feb 13, 1989•7 citations

Rigorous solution of a two-dimensional Blume-Emery-Griffiths model

Anders Rosengren, Roland Häggkvist

The spin-1 Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential (\ensuremath{\Delta}), a model introduced by Blume, Emery, and Griffiths (BEG), is studied on a honeycomb lattice. The exact solution of the BEG model is obtained for a certain relation K=K(J). Also an approximate treatment of the BEG model outside the surface, in the space of coupling constants, given by the relation above is discussed. Finally a digression is made on the critical temperature of the spin-1 Ising model.

Physical Review Letters•Aug 7, 1989•29 citations

Pair Correlation Functions of the Ising Type Model with Spin 1 within Two-Particle Cluster Approximation

O. R. Baran, Р. Р. Левицкий

The Blume-Emery-Griffiths model on hypercubic lattices within the two-particle cluster approximation is investigated. The expressions for the pair correlation functions in q-space are derived. On the basis of obtained results (at q = 0) the static susceptibility of this model on the simple cubic lattice is calculated at various values of the single-ion anisotropy and biquadratic interaction.

arXiv:1905.07586•physica status solidi (b)•Jun 1, 2000•11 citations

Monte Carlo Study of a Spin-3/2 Blume-Emery-Griffiths Model on a Honeycomb Lattice

We study the phase diagram of the spin-3/2 Blume-Emery-Griffiths model on a honeycomb lattice by Monte Carlo simulations in order to verify the presence of some peculiar features predicted by the effective field theory (EFT) with correlations. The locations of the order-disorder phase boundaries are estimated from thermal varia-tions of the magnetic susceptibility curves. It is found that for positive values of the biquadratic interactions the critical boundary shows a discontinuous character as a function of the single-ion anisotropy strength, in line with the EFT expectations. However, for negative values of the biquadratic interactions the step-like variation of the critical frontier predicted by EFT was not reproduced.

•Feb 16, 2016•3 citations

Phase Diagrams of the Diluted Spin‐3/2 Blume‐Capel Model

Abderrahmane Bakkali, M. Kerouad, M. Saber

Abstract The phase diagrams of the diluted spin‐3/2 Blume‐Capel Ising model on a honeycomb lattice are examined in detail, within the framework of an effective field theory based on the use of a probability distribution that correctly accounts for the single site kinematic relations. The thermal variation of the magnetization, the quadrupolar moment, and the higher‐order moment near critical concentrations are also investigated.

physica status solidi (b)•Dec 1, 1994•7 citations

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

J. Ricardo de Sousa, I. P. Fittipaldi

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen–Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N′=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal–Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

Journal of Applied Physics•May 15, 1994•15 citations
The critical temperature for an isotropic Blume-Emery-Griffiths model is discussed in a new type of effective-field approximation. The method, which can systematically include correlation effects, is illustrated by applying to a linear, honeycomb, and simple-cubic lattices. The relation between the present method and that very recently proposed by Chakraborty is widely discussed.
The spin-1 Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential (\ensuremath{\Delta}), a model introduced by Blume, Emery, and Griffiths (BEG), is studied on a honeycomb lattice. The exact solution of the BEG model is obtained for a certain relation K=K(J). Also an approximate treatment of the BEG model outside the surface, in the space of coupling constants, given by the relation above is discussed. Finally a digression is made on the critical temperature of the spin-1 Ising model.
We study the phase diagram of the spin-3/2 Blume-Emery-Griffiths model on a honeycomb lattice by Monte Carlo simulations in order to verify the presence of some peculiar features predicted by the effective field theory (EFT) with correlations. The locations of the order-disorder phase boundaries are estimated from thermal varia-tions of the magnetic susceptibility curves. It is found that for positive values of the biquadratic interactions the critical boundary shows a discontinuous character as a function of the single-ion anisotropy strength, in line with the EFT expectations. However, for negative values of the biquadratic interactions the step-like variation of the critical frontier predicted by EFT was not reproduced.
A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen–Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N′=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal–Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.