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

Nonequilibrium dynamics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic system with a time dependent oscillating magnetic field source

“…In order to have a general overview about it, it is beneficial to classify the studies in two categories based on the investigation of equilibrium and nonequilibrium phase transition properties of such type of mixed spin systems. In the former group, static or equilibrium properties of these type of systems have been analyzed within the several frameworks such as exact 9,10 , effective field theory with correlations [11][12][13][14][15][16][17][18][19][20][21][22] , Bethe lattice [23][24][25][26] , exact star-triangle mapping transformation 27 , high temperature series expansion method 29 , multisublattice Green-function technique 30 , Oguchi approximation 31 as well as Monte Carlo simulation 32 . It is underlined in the some studies noted above that when the system includes only the nearest-neighbor interaction between spins and the single-ion anisotropy, the temperature variation of resultant magnetization does not exhibit a compensation behavior.…”

The critical behaviors and the phase diagram of the mixed spin‐1/2 and spin‐2 Ising system on the Bethe lattice

“…It should be mentioned that the choice of the central spin has no effect on the system, that is the behavior of the system parameters do not change whether one chooses the spin-1/2 or spin-2 as the central spins Ref. [20,29]. Now we define,…”

“…Maybe the simplest of these is the mixed spin-1/2 and spin-1 Ising system and has been studied with many techniques including the renormalization-group technique [2], high-temperature series expansions [3], the free-fermion approximation [4], the recursion method on the Bethe lattice [5], the Bethe-Peierls approximation [6], the framework of the effectivefield theory [7,8], the mean-field approximation [9,10], the finite cluster approximation [11], the Monte-Carlo simulation [12,13], the mean-field renormalization-group technique [14], a numerical transfer matrix study [13] and the cluster variation method in pair-approximation [15]. The next possibility, including spin-1/2, is the mixed spin-1/2 and spin-3/2 Ising systems and includes the works with the transverse Ising model with a crystal field within the framework of the effective-field theory with correlations on the honeycomb lattice [16], on a square lattice by using the effective-field theory [17,18], again on a square lattice with a Monte Carlo algorithm [19] and on the Bethe lattice by using exact recursion relations [20]. Of course, the next possible mixing with spin-1/2 is with spin-2.…”

The phase diagrams of the mixed spin‐3/2 and spin‐5/2 Ising system on the Bethe lattice

“…Maybe the simplest of these for the mixing of the half-integer spins includes spin-1/2 and spin-3/2; this was studied within the framework of the effective-field theory [2] and with correlations on the honeycomb lattice [3], on a square lattice by using the effective-field theory [4,5] and for the Heisenberg ferrimagnetic model by the use of Green functions [6], again on a square lattice with a Monte Carlo algorithm [7], on the Bethe lattice with the coordination numbers 3 q = , 4, 5 and 6 [8], again within the effective-field theory with correlations with a random field [9] and using an effective-field method within the framework of a single-site cluster theory with independent transverse fields [10], but no interesting behaviors were observed since this mixedspin system only exhibits second-order phase transitions except for the case with a random magnetic field [9]. The next possible mixing of the half-integer spins is the mixing of the spin-1/2 and spin-5/2 system; unfortunately, this system was not studied as far to our knowledge but, in any case, even if we do not present the phase diagram of this system here, we have studied this mixed-spin system in the search for any interesting critical behavior.…”