Magnetic properties of the mixed spin-5/2 and spin-3/2 Blume-Capel Ising system on the two-fold Cayley tree

• Authors: Rachidi Yessoufou , Saliou Amoussa , Felix Hontinfinde
• Languages of publication: EN

Abstracts

EN

We use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions Δ1 and Δ2 are considered for the sublattice with spin-5/2 and spin-3/2 respectively. For different coordination numbers q of the Cayley tree sites, the phase diagrams of the model are presented with a special emphasis on the case q = 3, since other values of q reproduce similar results. First, the T = 0 phase diagram is illustrated in the (D
A = Δ1/J,D
B = Δ2/J) plane of reduced crystal-field interactions. This diagram shows triple points and coexistence lines between thermodynamically stable phases. Secondly, the thermal variation of the magnetization belonging to each sublattice for some coordination numbers q are investigated as well as the Helmoltz free energy of the system. First-order and second-order phase transitions are found. The second-order phase transitions become sharper and sharper when D
A or D
B increases. The first-order transitions only exist for some appropriate non-zero values of D
A and/or D
B. The corresponding transition lines never connect to the second-order transition lines. Thus, the non-existence of tricritical points remains one of the key features of the present model. The magnetic exponent β
0 of the model is estimated and found to be ¼ at small values of D
A = D
B = D and β
0 = ½ at large values of D. At intermediate values of D, there is a crossover region where the magnetic exponent displays interesting behaviours.

Keywords

EN

mixed spin model; two-fold cayley tree; recursion relations; magnetization; phase transition

Discipline

• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)
• 05.70.Ce: Thermodynamic functions and equations of state(see also 51.30.+i Thermodynamic properties, equations of state in physics of gases; for equations of state of specific substances, see 64.30.-t; for equations of state of nuclear matter, and of neutron-star matter, see 21.65.Mn and 26.60.Kp, respectively; see also 95.30.Tg in astronomy; for thermodynamic properties of superconductors, see 74.25.Bt)
• 64.60.Cn: Order-disorder transformations(see also 81.30.Hd Constant-composition solid-solid phase transformations: polymorphic, massive, and order-disorder in materials science; for effects of disorder on superconducting transition temperature, see 74.62.En)
• 75.10.Hk: Classical spin models
• 75.30.Gw: Magnetic anisotropy

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2009
• Volume: 7
• Issue: 3
• Pages: 555-567

Dates

published

1 - 9 - 2009

online

25 - 6 - 2009

Contributors

author

Rachidi Yessoufou

• Département de Physique (FAST) et Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi, 01 BP 613, Porto-Novo, Bénin

author

Saliou Amoussa

• Département de Physique (FAST) et Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi, 01 BP 613, Porto-Novo, Bénin

author

Felix Hontinfinde

• Département de Physique (FAST) et Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi, 01 BP 613, Porto-Novo, Bénin

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Identifiers

DOI

10.2478/s11534-009-0016-x