The study of magnetization of the spin system in the ground state

Variational-method study of the spin-1 Ising model with biaxial crystal-field anisotropy

“…Thus, we may conclude that the Ising model with a transverse crystal-field exhibits a TCP on the τ versus δ x curve, when the transverse crystal field δ y is null. This is in contrast to EFT results for coordination numbers z = 3, 4 and 6 9,10,11,12,13 , for which no TCP is found for any value of δ y . .…”

“…On the other hand, some studies have dealt with the effect of a transverse crystalfield 9,10,11,12,13 . In particular, the presence of a transverse crystal-field in the BC model may change the nature of the phase transition, due to quantum effects.…”

“…On the other hand, theoretical studies of the Hamiltonian described by Eq. ( 3), using effective-field theory (EFT) 9,10,11,12,13 So, we study here the model described by Eq. ( 3), which we treat by employing the variational approach based on the Bogolyubov inequality for the free energy.…”

“…. Some authors 12,13 have used the condition a 2 = 0 and a 4 < 0 to determinate the firstorder line, but this condition corresponds to the stability line of the P phase. One can note that it is not possible to calculate first-order lines based on the equation of state ( 9) alone, because in this case one has m = 0 at the transition point.…”

First-order quantum phase transition in an anisotropic Ising model with infinite-range random interaction

“…͑3͒ has been studied by using the effective-field theory ͑EFT͒. [50][51][52][53][54] The appearance of this anisotropy has been demonstrated experimentally by changing the thickness of the nonmagnetic TaN interlayer in FeTaN/ TaN/ FeTaN sandwiches. 55 Jiang and Wang 56 have included in the Eq.…”