Re-entrant ferromagnetism in a two-dimensional mixed spin Ising model with random nearest-neighbour interactions

The transverse spin-1 Ising model with random interactions

“…Moreover, there appear different thresholds as solutions of T/J ¼ 0 (namely: (1Àp) c ¼ 0.2495, 0.3676, 0.3904, and 0.5269 at a ¼ À1.0, À0.75, À0.5, and À0.1, respectively). Such a non-uniform convergence of T c /J as a function of (1Àp) and for ao0 is also obtained in a random bond mixed spin-1 2 and spin-1 Ising ferromagnet [60][61][62]. It is seen from curve (e) that the phase diagram exhibits a reentrant behavior in the region 0.400opo0.473 which results from the competition between the fluctuations induced by the temperature and the exchange interaction terms.…”

Thermodynamical properties of the random field mixed spin transverse Ising model

“…For a given configuration of the random fields, the internal energy U sS of the system described by the Hamiltonian (1) is given by where P s ¼ P % z i¼1 s z i ; and N is the total number of magnetic atoms. In order to calculate P s S z 0 ; we substitute G 0 ¼ P s in (36). Then it can be written as…”

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

“…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].…”