Abstract 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.
The ferromagnetic spin-2 quantum Blume-Capel model in the presence of a transverse crystal field interaction is studied by employing a variational approach based on Bogoliubov inequality for the free energy and an exact mapping of the ground state. The thermodynamic properties have been obtained using a single spin cluster, which is equivalent to the usual mean-field approximation. The temperature dependence of the magnetization has been analyzed and the global phase diagram, as function of the model parameters, has been obtained for any values of the coordination number of the lattice. A variety of quantum phase transitions, multiple and multicritical points, are present in several topologies of the corresponding phase diagrams. The ground state properties of the system have also been obtained through an exact mapping of the spin-2 model onto another equivalent spin-1 Blume-Capel model in a transverse field. This mapping allows one to determine an exact asymptote formula of the phase diagram at zero temperature in the limit of large longitudinal crystal field for any lattice dimension.
We study the one-dimensional S = 1 Blume-Emery-Griffiths model.Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism.We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators.Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve.In the neighborhood of the endpoints of the intermediate plateau, the specific heat shows a double peak structure.
The mapping transformation technique is applied to obtain exact results for the spin-1/2 and spin- S ( S = 1/2, 1) Ising–Heisenberg antiferromagnetic chain in the presence of an external magnetic field. Within this scheme, a field-induced first-order metamagnetic phase transition resulting in multiplateau magnetization curves is investigated in detail. It is found that the scenario of the plateau formation depends fundamentally on the ratio between Ising and Heisenberg interaction parameters, as well as on the strength of the XXZ Heisenberg exchange anisotropy.
We generalize a class of Heisenberg antiferromagnets in one, two, and three dimensions, which have been shown to exhibit magnetization plateaus for spin-
21. In a certain parameter range of the general model, which is formally defined in
D dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-
S result reproduces the known cases for spin-
21 in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-
1 model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results.