Erhan Albayrak

Mixed spin- and spin-1 Blume-Capel Ising ferrimagnetic system on the Bethe lattice

We present the exact formulation for the mixed spin-12 and spin-32 Blume–Capel Ising ferrimagnetic system on the Bethe lattice by the use of exact recursion relations. The exact expressions for the magnetization, quadrupole moment, Curie temperature and free energy are found and the phase diagrams are illustrated on the Bethe lattice with the coordination numbers q=3, 4, 5 and 6. It is found that the phase diagram of this mixed spin system only presents second-order phase transitions. The thermal variation of the magnetization belonging to each sublattice and the net magnetization are also presented.

Phase diagrams of the spin- Blume–Emery–Griffiths model on the Bethe lattice using the recursion method

Abstract The statistical physics of the spin- 3 2 Blume–Emery–Griffiths model on the Bethe lattice is studied by using the exact recursion equations. Exact expressions for the free energy, the Curie or the second-order phase transition temperatures as well as the magnetization and quadrupolar moment order parameters are found. The phase diagrams in ( kT / J , D / J ) and ( kT / J , K / J ) planes are presented in depth for various values of constants K / J and D / J , respectively. The phase diagrams are discussed and a comparison is made with the results of the other approximation methods.

The spin-3/2 Blume-Capel model on the Bethe lattice using the recursion method

Abstract The spin-3/2 Blume–Capel model is solved on the Bethe lattice using the exact recursion equations. The nature of the variation of the Curie temperature with the ratio of the single-ion anisotropy term to the exchange-coupling constant is studied and the phase diagrams are constructed on the Bethe lattice with the co-ordination numbers q =3 and 6. A comparison is made with the results of the other approximation schemes.

Mixed spin-12 and spin-32 Blume–Capel Ising ferrimagnetic system on the Bethe lattice

We present the exact formulation for the mixed spin-12 and spin-32 Blume–Capel Ising ferrimagnetic system on the Bethe lattice by the use of exact recursion relations. The exact expressions for the magnetization, quadrupole moment, Curie temperature and free energy are found and the phase diagrams are illustrated on the Bethe lattice with the coordination numbers q=3, 4, 5 and 6. It is found that the phase diagram of this mixed spin system only presents second-order phase transitions. The thermal variation of the magnetization belonging to each sublattice and the net magnetization are also presented.

Multicritical phase diagrams of the spin- Blume–Emery–Griffiths model on the Bethe lattice using the recursion method

Abstract The multicritical behaviour of the spin- 3 2 Blume–Emery–Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field is studied on the Bethe lattice by introducing two-sublattices A and B within the exact recursion equations. Exact expressions for the free energy, the Curie or second-order phase transition temperatures, as well as for the magnetization and quadrupolar moment order parameters are obtained. The general procedure of investigation of critical properties is discussed and phase diagrams are obtained, in particular, for negative biquadratic couplings. The phase diagrams of the model exhibits a rich variety of behaviours. Results are compared with other approximate methods.

MIXED SPIN-1 AND SPIN-

The mixed spin-1 and spin- Blume–Capel Ising ferrimagnetic system for the central spin with spin-1 is studied on the Bethe lattice using the exact recursion equations. The exact expressions for the magnetization, the quadrupolar moment, the Curie temperature and the free energy are found and the phase diagrams are constructed on the Bethe lattice with the coordination numbers q = 3, 4 and 6 for the various values of the single-ion anisotropy constants dA = DA/J for spin-1 and dB = DB/J for spin-. The existence of a tricritical point is investigated for different values of q and the single-ion anisotropy constants. The phase diagrams in the (kTc/J, dA) plane for the central spin are obtained for two different cases; (1) dA = dB and (2) dA is varied for selected values of dB. The results are compared with those of other approximate methods.

\frac{3}{2}

Exact expressions for the magnetization or the dipole moment, the quadrupolar moment and the Curie temperature of the spin-3/2 Blume–Capel model on the Bethe lattice are derived using the recursion method. The thermal variations of the magnetization and quadrupolar moment order parameters are studied in depth for a range of the coupling parameter, α=D/J, and a number of characteristic behaviors for their thermal variations are obtained. Besides the stable branches of the order parameters, we find the unstable branches of them which occur at low temperatures and near the first- and second-order phase-transition temperatures. Finally, the phase diagram and the critical behavior of the model are discussed.

BLUME–CAPEL ISING FERRIMAGNETIC SYSTEM ON THE BETHE LATTICE

Abstract The Blume–Emery–Griffiths model Hamiltonian with the transverse crystal field interaction (Δ), the transverse ( Ω ) and longitudinal (h) external magnetic fields in addition to the usual exchange interactions both bilinear (J) and biquadratic (K) and the crystal-field interaction (D) is studied via the scheme of mean-field approximation. Thermal variation of the longitudinal and transverse dipolar (S) and quadrupolar (Q) order parameters of the model is investigated extensively for the various values of the interaction parameters. Besides the stable solutions, metastable and unstable solutions of the order parameters are also found. In the absence of the longitudinal external magnetic field, the phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths and the system parameters in the five different planes. A comparison with other approximate techniques is also made.

Statistical mechanics of the spin-3/2 Blume–Capel model on the Bethe lattice using the recursion method

Abstract The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume–Emery–Griffiths model on the simple cubic lattice with dipole–dipole, quadrupole–quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made.

Phase diagrams of the Blume–Emery–Griffiths model calculated by the mean-field approximation including the transverse fields effects

The random crystal field (RCF) effects are investigated on the phase diagrams of the mixed-spins 1/2 and 3/2 Blume-Capel (BC) model on the Bethe lattice. The bimodal random crystal field is assumed and the recursion relations are employed for the solution of the model. The system gives only the second-order phase transitions for all values of the crystal fields in the non-random bimodal distribution for given probability. The randomness does not change the order of the phase transitions for higher crystal field values, i.e., it is always second-order, but it may introduce first-order phase transitions at lower negative crystal field values for the probability in the range about 0.20 and 0.45, which is only the second-order for the non-random case in this range. Thus our work claims that randomness may be used to induce first-order phase transitions at lower negative crystal field values at lower probabilities.