The critical behavior of the mixed spin-1 and spin-2 Ising ferromagnetic system on the Bethe lattice (original) (raw)
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The phase diagrams of the mixed spin-3/2 and spin-5/2 Ising system on the Bethe lattice
Physica Status Solidi B-basic Solid State Physics, 2007
In this paper we study the critical behaviors of the half-integer mixed spin-3/2 and spin-5/2 Blume–Capel Ising ferrimagnetic system by using the exact recursion relations on the Bethe lattice for q = 4 and 6, whose real lattice correspondences are square and simple cubic lattices, respectively. We have obtained the phase diagrams in the (kTc/|J |, DA/|J |) planes for constant values of DB/|J |, the reduced crystal field of the sublattice with spin-5/2, and in the (kTc/|J |, DB/|J |) planes for constant values of DA/|J |, the reduced crystal field of the sublattice with spin-3/2. Even if the system presents both second- and first-order phase transitions, their lines never connect to each other and end at critical points; thus, no tricritical points are observed. We have also found the existence of one or two compensation temperatures for appropriate values of the crystal fields, therefore observing reentrant behavior for some of the compensation lines. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Mixed spin-3/2 and spin-5/2 Ising system on the Bethe lattice
Physics Letters A, 2006
In order to study the critical behaviors of the half-integer mixed spin-3/2 and spin-5/2 Blume-Capel Ising ferrimagnetic system, we have used the exact recursion relations on the Bethe lattice. The system was studied for the coordination numbers with q = 3, 4, 5 and 6, and the obtained phase diagrams are illustrated on the (kT c /|J |, D A /|J |) plane for constant values of D B /|J |, the reduced crystal field of the sublattice with spin-5/2, and on the (kT c /|J |, D B /|J |) plane for constant values of D A /|J |, the reduced crystal field of the sublattice with spin-3/2, for q = 3 only, since the cases corresponding to q = 4, 5 and 6 reproduce results similar to the case for q = 3. In addition we have also presented the phase diagram with equal strengths of the crystal fields for q = 3, 4, 5 and 6. Besides the second-and first-order phase transitions, the system also exhibits compensation temperatures for appropriate values of the crystal fields. In this mixed spin system while the second-order phase transition lines never cut the reduced crystal field axes as in the single spin type spin-3/2 and spin-5/2 Ising models separately, the first-order phase transition lines never connect to the second-order phase transition lines and they end at the critical points, therefore the system does not give any tricritical points. In addition to this, this mixed-spin model exhibits one or two compensation temperatures depending on the values of the crystal fields, as a result the compensation temperature lines show reentrant behavior.
Mixed spin-5/2 and spin-2 Ising ferrimagnetic system on the Bethe lattice
Journal of Magnetism and Magnetic Materials, 2015
The magnetic properties of spins-S and Ising model on the Bethe lattice have been investigated by using the Monte Carlo simulation. The thermal total magnetization and magnetization of spins S and with the different exchange interactions, different external magnetic field and different temperatures have been studied. The critical temperature and compensation temperature have been deduced. The magnetic hysteresis cycle of Ising ferrimagnetic system on the Bethe lattice has been deduced for different values of exchange interactions between the spins S and , for different values of crystal field and for different sizes. The magnetic coercive filed has been deduced.
Acta Physica Polonica A, 2017
The effect of uniaxial single-ion anisotropy on magnetic and critical properties of the mixed spin-1/2 and spinS (S > 1/2) Ising model on a three-coordinated Bethe lattice is rigorously examined with the help of star-triangle transformation and exact recursion relations. In particular, our attention is focused on the ferrimagnetic version of the model, which exhibits diverse temperature dependences of the total and both sublattice magnetizations. It is shown that the critical behavior of the mixed-spin Ising model on the Bethe lattice basically depends on whether the quantum spin number S is integer or half-odd-integer.
Physica A-statistical Mechanics and Its Applications, 2010
The temperature-dependent phase diagrams of the spin-3/2 Ising model on a two-layer Bethe lattice with ferromagnetic (FM)/antiferromagnetic (AFM) intra-layer and either FM or AFM type inter-layer interactions are investigated under a constant magnetic field (H) and in the presence of a crystal field (D) by using exact recursion equations in a pairwise approach for coordination numbers q = 3, 4 and 6, in detail. In the light of the groundstate (GS) phase diagrams, the temperature-dependent phase diagrams of the model are obtained by studying the thermal variations of the order parameters, response functions and free energy. Then, they are illustrated on the (kT /) planes for the given system parameters. It is observed that the system exhibits first-and second-order phase transitions for all q values, and hence, in some cases, tricritical points. The existence of critical-end points and that of isolated points are also observed. The re-entrant behavior owes its presence to the two Néel temperatures, T N , that are present for all q.
Physica A: Statistical Mechanics and its Applications, 2012
Mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration-iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.
The Phase Diagrams of Spin-1/2 Ising Model on a Two-Layer Bethe Lattice with AFM/AFM Interactions
Acta Physica Polonica A
The phase diagrams of spin-1/2 Ising model on a two-layer Bethe lattice with antiferromagnetic interactions for each layer and either antiferromagnetic or ferromagnetic interaction between the layers are investigated by using the pairwise approach for given values of coordination number q. The exact expressions of the order-parameters, response functions and free energy are obtained in terms of the recursion relations. The ground-state phase diagrams are calculated for given system parameters of the model. In the guidance of the ground-state phase diagrams, the temperature dependent phase diagrams of the model are also studied in detail for given coordination numbers q = 3, 4 and 6. It was found that the system presents only second-order phase transitions with different thermal behaviors for all values of q. In addition, two Néel temperatures, T N , are found for q = 6 only.
The spin-1 Ising model on a two-layer Bethe lattice with FM/AFM interactions
Journal of Magnetism and Magnetic Materials, 2009
Two-layer Bethe lattice whose lattice sites are occupied with spin-3/2 atoms is solved exactly by using the recursion relations in a pairwise approach for given coordination numbers q = 3, 4 and 6 with equal external magnetic fields acting on the layers. The ferromagnetic (FM) and antiferromagnetic (AFM) interactions for the spins of the upper and lower layers, respectively, and either FM or AFM type interactions between the adjacent spins of the layers are assumed. The phase diagrams of the model are studied on different planes for given system parameters by obtaining the ground state (GS) phase diagrams and the thermal variations of the order parameters and the response functions, i. e. the susceptibility and the specific heat, in detail. It was found that the model presents both second-and first-order phase transitions. The reentrant behavior is seen when the model presents two Néel temperatures for higher q values. The existence of the tricritical point and critical end points is also confirmed.
Chinese Physics B, 2011
The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or antiferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Néel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.
Journal of Statistical Physics, 2007
The critical and compensation temperatures of the bilayer Bethe lattices with one of the layers having only spin-1/2 atoms and the other having only spin-1 atoms placed symmetrically are studied by using exact recursion relations in a pairwise approach. The Hamiltonian of the model consist of the bilinear intralayer coupling constants of the two layers J 1 and J 2 for the interactions of the atoms in layers with spin-1/2 and spin-1, respectively, and the bilinear interlayer coupling constant J 3 between the adjacent atoms with spin-1/2 and spin-1 of the layers. After obtaining the ground state phase diagram with J 1 > 0, the variations of the order-parameters and the free energy are investigated to obtain the phase diagram of the model by considering only the ferromagnetic ordering of the layers, i.e. J 1 > 0 and J 2 > 0, and ferromagnetic or antiferromagnetic ordering of the adjacent spins of the layers, J 3 > 0 or J 3 < 0, respectively. It was found that the system presents both second-and first-order phase transitions and, tricritical points. The compensation temperatures was also observed for the appropriate values of the system parameters.