Phase Diagram for Ashkin-Teller Model on Bethe Lattice

Using- the recursion method, we study the phase transitions of theAshkin-Teller model on the Bethe lattice, restricting ourselves to the case of ferromagneticinteractions. The isotropic Ashkin-Teller model and the anisotropic one are respectivelyinvestigated, and exact expressions for the free energy and the magnetization are obtained. It canbe found that each of the three varieties of phase diagrams, for the anisotropic Ashkin-Tellermodel, consists of four phases, i.e., the fully disordered paramagnetic phase Para, the fullyordered ferromagnetic phase Ferro, and two partially ordered ferromagnetic phases 【 σ 】 and 【 σs】, while the phase diagram, for the isotropic Ashkin-Teller model, contains three phases, i.e., thefully disordered paramagnetic phase Para, the fully ordered ferromagnetic phase Baxter Phase, andthe partially ordered ferromagnetic phase 【 σs 】.

Magnetic phase diagrams of Fe–Mn–Al alloy on the Bethe lattice

The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction（J） distribution in the Blume–Capel（BC） model. Ferromagnetic（J 〉 0） or antiferromagnetic（J 〈 0）bonds or dilution of the bonds（J = 0） are assumed between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic（F）, antiferromagnetic（AF）, paramagnetic（P）, or spin-glass（SG） phases from the possible other one. In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained.

Bond Dilution Effects on Bethe Lattice the Spin-1 Blume–Capel Model

The bond dilution effects are investigated for the spin-1 Blume-Capel model on the Bethe lattice by using the exact recursion relations. The bilinear interaction parameter is either turned on ferromagnetically with probability p or turned off with probability 1 - p between the nearest-neighbor spins. The thermal variations of the order-parameters are studied in detail to obtain the phase diagrams on the possible planes spanned by the temperature （T）, probability （p） and crystal field （D） for the coordination numbers q = 3, 4, and 6. The lines of the second-order phase transitions, To-lines, combined with the first-order ones, Tt-lines, at the tricritical points （TCP） are always found for any p and q on the （T, D）-planes. It is also found that the model gives only Tc-lines, To-lines combined with the Tt-lines at the TCP＇s and only Tt-lines with the consecutively decreasing values of D on the （T, p）-planes for aJ1 q.

Spin-3/2 Ising model AFM/AFM two-layer lattice with crystal field

The spin-3/2 Ising model is investigated for the case of antiferromagnetic （AFM/AFM） interactions on the two- layer Bethe lattice by using the exact recursion relations in the pairwise approach for given coordination numbers q=3, 4 and 6 when the layers are under the influences of equal external magnetic and equal crystal fields. The ground state （GS） phase diagrams are obtained on the different planes in detail and then the temperature-dependent phase diagrams of the system are calculated accordingly. It is observed that the system presents both second- and first-order phase transitions for all q, therefore, tricritical points. It is also found that the system exhibits double-critical end points and isolated points. The model also presents two Neel temperatures, TN, and the existence of which leads to the reentrant behaviour.

The mixed-spins 1/2 and 3/2 Blume-Capel model with a random crystal field

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.

Critical properties of mixed spin-1 and spin-5/2 with equal and unequal crystal fields

The effects of assuming equal or unequal crystal fields （CF） on the phase diagrams of a mixed spin-1 and spin-5/2 system are investigated in terms of the recursion relations on the Bethe lattice （BL）. The equal CF case was considered for the coordination numbers q = 3,4, and 6, while for q = 3 the unequal CF case was also studied. It was found that for the equal CF case, the model exhibits second-order phase transitions and two compensation temperatures for all q, the reentrant behavior for q = 4 and first-order phase transitions and tricritical point （TCP） for q = 6. In the unequal CF case for q = 3, the system yields first- and second-order phase transitions, TCP＇s, and three compensation temperatures. In addition, the TCP＇s in a very short range are classified as the stable and unstable ones depending on their free energies.