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

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Özkan A., Kutlu B.

Open Physics

2011

vol. 9

issue 3

884-890

The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($$ \ell = \frac{I} {J} $$) 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 (ℓ). The dipole-quadrupole critical exponent δχ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $$ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 $$ for $$ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 $$ and $$ h = \frac{H} {J} = 0 $$ parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δℓ are in good agreement with the universal value (δh = 5) of the external magnetic field.

The ferrimagnetic phase of the Blume-Emery-Griffiths model on the cellular automaton

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Seferoğlu N., Kutlu B.

Open Physics

2008

vol. 6

issue 2

230-237

The Blume-Emery-Griffiths model is simulated using the cooling algorithm which is improved from the Creutz cellular automaton (CCA) under periodic boundary conditions. The simulations are carried out on a simple cubic lattice at K/J = −1.5 in the range of −3.5 < D/J < 0.5, with J and K representing the nearestneighbour bilinear and biquadratic interactions, D being the single-ion anisotropy parameter. The phase diagram characterizing phase transition of the model is obtained. We found different kinds of phase transitions between the ferromagnetic, quadrupolar, staggered quadrupolar and ferrimagnetic phases for K/J = −1.5. In particular, the region of the phase diagram containing a ferrimagnetic phase is explored and compared to those obtained by other methods. The simulations confirm that the ferrimagnetic phase occurs in the narrow interval −3.006 ≤ D/J < −3. This result is in a good agreement with Monte Carlo renormalization group and closer to the cluster variation method result than the mean field approximation result.

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2 Open Physics

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1 2008

2 Kutlu B.

1 Seferoğlu N.

1 Özkan A.

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

The ferrimagnetic phase of the Blume-Emery-Griffiths model on the cellular automaton