A spin-one Ising model with single-ion anisotropy and biquadratic exchange on a Bethe lattice

Multicritical phase diagrams of the Blume–Emery–Griffiths model with repulsive biquadratic coupling including metastable phases: the pair approximation and the path probability method with pair distribution

“…Later on it has been studied by the MC method [15], the Monte Carlo Renormalization group [16], the MFA [17], the RG [18], the CVM [1,6] and the two-particle cluster approximation [19]. The BEG model with repulsive biquadratic coupling was also solved on the Bethe lattice using the exact recursion equations [20].…”

“…(20). Solutions of these dynamic equations are given by two different methods: the first one is the Runge-Kutta method.…”

“…(19) into Eq. (17), the set of dynamic or the rate equations for the bond variables are obtained: (20) where e A ij , e B ij and Y A ij , Y B ij and Z A and Z B are given in Eq. (15).…”

Phase Diagrams of the Spin-1 Blume–emery–griffiths Model in a Random Transverse Field

“…First, A α 0,v (N, Ω 0 ) and B α 0,v (N, Ω 0 ) are got by setting r = v in Eqs. (36) and (37), that is,…”

“…24,25 The phase diagrams of the BEG model for 0 ≤ K/J have been studied by the mean field approximation, [26][27][28] the position space renormalization group method, 29 the cluster variation method, 30,31 series-expansion methods, 32 the transfer-matrix method, 33 the constant coupling approximation, 34 the linear-chain approximation, 35 and on the Bethe lattice using exact recurring equations. 36 On the other hand, the BEG model with repulsive biquadratic coupling i.e., K/J < 0 was a subject of interest of many authors. [37][38][39][40][41] These studies have shown a variety of interesting features as, for example, single and double reentrancy regions and ferrimagnetic phases.…”