Re-entrant phase transitions of the Blume-Emery-Griffiths model

Kasono, Katsumi; Ono, Ikuo

doi:10.1007/bf01323573

Cited by 32 publications

(38 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The global MFA analysis [6] on this lattice showed a number of other remarkable features such as doubly reentrant behaviour and a ferrimagnetic phase which appears between the staggered quadrupolar phase and the ferromagnetic phase. Latter investigations [8][9][10][11][12] mainly confirmed these results. Using exact solution on the Bethe lattice [13] have constructed the full set of phase diagrams for spin-1 Ising model for both positive and negative biquadratic coupling.…”

Section: Introductionsupporting

confidence: 75%

“…The staggered quadrupolar phase, also called staggered quadrupollar phase, was predicted and investigated on the square lattice by means of mean-field approximation (MFA) and by Monte Carlo (MC) simulations [5]. The transition from the staggered quadrupolar phase to the ferromagnetic phase was established on a three-dimensional cubic lattice [6][7][8]. The global MFA analysis [6] on this lattice showed a number of other remarkable features such as doubly reentrant behaviour and a ferrimagnetic phase which appears between the staggered quadrupolar phase and the ferromagnetic phase.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Phase diagrams of the Blume-Emery-Griffiths thin films

2006

View full text Add to dashboard Cite

We study the spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field, using the mean field theory. In addition to the four usual phases: The disordered phase D, the ferromagnetic phase F, the staggered quadrupolar phase SQ and The ferrimagnetic phase I, we found two new phases, in the case of a thin magnetic film, namely: the sublattice (A or B) non magnetic phase NM and the global non magnetic phase G. These phases are studied, for each layer of the film in the temperature-crystal field plane (T /J, ∆/J) for different film thicknesses. It is found that the ferrimagnetic and sublattice phases are absent for a monolayer film. Whereas, these phases appear for increasing film thicknessses N ≥ 2. On the other hand, the thermal behaviour of the layer quadrupolar moments q A , q B and layer magnetisations m A , m B are investigated for negative values of the biquadratic coupling and crystal field. It is also shown that for fixed values of the biquadratic coupling, the temperature and the crystal field, each layer of the film can belong to a different phase. To illustrate this situation, an example is given for d/J = −1.5, ∆/J = −3.0 and T /J = 1.3.

show abstract

Section: Introductionsupporting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Phase diagrams of the Blume-Emery-Griffiths thin films

2006

View full text Add to dashboard Cite

show abstract

“…ter values (6,12,13,16) , where z is the coordination number. Sec.2, the results are discussed in Sec.3 and a conclusion is given in Sec.4.…”

Section: Introductionmentioning

confidence: 99%

Re-entrant phase transitions of the Blume–Emery–Griffiths model for a simple cubic lattice on the cellular automaton

Seferoğlu¹,

Kutlu²

2007

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

. IntroductionThe Blume-Emery-Griffiths (BEG) model 1 was originally introduced in order to explain the phase separation and superfluidity in the He 3 -He 4 mixtures. Subsequently, the model was used in the description of a variety of different physical phenomena such as multicomponent fluids 2 , microemulsions 3 , and semiconductors alloys 4 , etc.The Hamiltonian of the BEG model is given by,where s i = ±1, 0 and < ij > denotes summation over all nearest-neighboring (nn) spin pairs on a simple cubic lattice. The parameters of J and K are the bilinear and biquadratic interaction energies, respectively and D is the single-ion anisotropy constant. The three-dimensional BEG model has been extensively studied by different techniques, using the mean-field approximation (MFA) (1,5−7) , effective-field theory (8−11) , two-particle cluster approximation (TPCA) 12 , Bethe approximation 13 , high-temperature series expansion 14 , renormalization group theory 15 , Monte Carlo simulations (13,16−17) , linear chain approximation (18,19) and cellular automaton (20,21) In this paper we studied the three-dimensional BEG model using an improved heating algorithm from the Creutz Cellular Automaton (CCA) for simple cubic lattice. The CCA algorithm is a microcanonical algorithm interpolating between the canonical Monte Carlo and molecular dynamics techniques on a cellular automaton, and it was first introduced by Creutz 22 .In the previous papers (20,21,23−26) , the CCA algorithm and improved algo-2 rithms from CCA were used to study the critical behavior of the different Ising model Hamiltonians on the two and three-dimensions. It was shown that they have successfully produced the critical behavior of the models.The BEG model has a complicated phase diagrams and has several kinds of phase transitions, such as re-entrant and double re-entrant transitions for some values of the model parameters on the three-dimensional lattices.However, there exists the differences between the phase diagrams in theter values (6,12,13,16) , where z is the coordination number. Sec.2, the results are discussed in Sec.3 and a conclusion is given in Sec.4. ModelThree variables are associated with each site of the lattice. The value of 3 each sites are determined from its value and those of its nearest-neighbors at the previous time step. The updating rule, which defines a deterministic cellular automaton, is as follows: Of the three variables on each site, the first one is Ising spin B i . Its value may be 0 or 1 or 2. The Ising spin energy for the model is given by Eq.1. In Eq.1, Si = Bi − 1. The second variable is for momentum variable conjugate to the spin (the demon). The kinetic energy associated with the demon, H k , is an integer, which equal to the changing in the Ising spin energy for the any spin flip and its values lie in the interval (0, m). The upper limit of the interval, m, is equal to 24J. The total energyis conserved.The third variable provides a checkerboard style updating, and so it allows the simulation of the Ising model on a cellu...

show abstract

“…For the model on the lattices with two interpenetrating sublattice, A and B, a novel ordered state called the staggered quadrupole (SQ) phase appears at low temperatures in the region J 2 =J 1 o À D=zJ 1 À 1 and D40 in the case of J 1 40 [1,2]. In the SQ phase ( Fig.…”

mentioning

confidence: 98%