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Newman, Kathie E.; Dow, John D.

doi:10.1103/physrevb.27.7495

Cited by 184 publications

(65 citation statements)

References 23 publications

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“…The calculations have been done on the different lattice sizes L = 4 6 8 9 and 12. The previous studies implied that the dipole-quadrupole interaction is a magnetic field-like perturbation in the spin-1 Ising model Hamiltonian [25,40]. Our simulations confirmed that the dipolequadrupole interaction parameter represses one of the spin states (S = +1 or −1) and it has broken the symmetry in the Hamiltonian.…”

Section: Resultssupporting

confidence: 76%

“…The parameters J, K , I, D and H are bilinear, biquadratic, dipole-quadrupole interaction terms, the single-ion anisotropy constant and the external field term. Some versions of the model have been applied to the physical systems such as the solid-liquid-gas systems [10], the multicomponent fluids [1], the microemulsions [22], the semiconductor alloys [25][26][27], He 3 -He 4 mixtures [16,17,26], the binary alloys [27] and the magnetic spin systems [28][29][30][31]. The aim of this study is to investigate the critical behavior of the BEG model with the dipole-quadrupole interaction ( ) and to estimate the power laws and the finite size scaling relations for the order parameter (M) and the susceptibility (χ) in the = have been taken zero ( = 0, = 0 and = 0).…”

Section: Introductionmentioning

confidence: 99%

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Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

Özkan

Kutlu

2011

Open Physics

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Abstract:The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ( = I J ) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction ( ). The dipole-quadrupole critical exponent δ has been estimated from the data of the order parameter (M) and the susceptibility (χ).

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Section: Resultssupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

Özkan

Kutlu

2011

Open Physics

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“…The spin-1 Ising model in the presence of crystal-field (D) which called as Blume-Capel (BC) model is one of the most actively studied higher spin Ising models in statistical physics due to the both theoretical importance and its application to different systems [1][2][3][4][5][6][7][8][9]. BC model has been studied with many different techniques, such as mean field approximation (MFA) [10], effective field theory (EFT) [11][12][13], Bethe approximation [14], Monte Carlo simulation (MCs) [15], renormalization group theory [16] and the cluster variational approximation [17,18], and it was found that it exhibits very interesting and rich critical phenomena.…”

Section: Introductionmentioning

confidence: 99%

Hysteresis and compensation behaviors of spin-3/2 cylindrical Ising nanotube system

Kocakaplan

Keskín

2014

Journal of Applied Physics

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An effective-field theory with correlations has been used to study the hysteresis, susceptibility and compensation behaviors of the spin-1 hexagonal Ising nanowire (HIN) with core-shell structure. The effects of the temperature, crystal field, core-shell interfacial coupling and shell surface coupling are investigated on hysteresis and compensation behaviors, in detail. When the core-shell interfacial coupling is weak, the double and triple hysteresis loops can be seen in the system. The hysteresis loops have different coercive field points that the susceptibility make peak at these points. Moreover, we observed that the system displays the Q-, R-, S-, P-, N-and W-types of compensation behaviors according to Neél classification nomenclature.Finally, the obtaining results are compared with some experimental and theoretical results and found a good agreement.

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“…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.…”

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

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. 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...

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Zinc-blende—diamond order-disorder transition in metastable crystalline(GaAs)1−xGe2x<

Cited by 184 publications

References 23 publications

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

Hysteresis and compensation behaviors of spin-3/2 cylindrical Ising nanotube system

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

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