The FM/AFM bilayer Bethe lattice with FM or AFM interlayer interactions

Abstract

The bilayer Bethe lattice with the Ising spins of the top layer having only ferromagnetic (FM) interactions and the spins of the bottom one having only antiferromagnetic (AFM) interactions were allowed to interact via the interlayer interaction either FM or AFM type. The problem was analyzed by using the exact 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 phase diagrams of the model were obtained on different planes for given system parameters by studying 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. The model with five distinct GS configurations presents only the second‐order phase transition lines, i.e. the lines of the Néel temperatures TN. Two TN's were obtained for q = 6 in the transition regions from the AFM phases to the FM phases at low temperatures, as a result the TN lines show reentrant behavior for q = 6. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Spin-3/2 Ising model on a two-layer Bethe lattice with FM/AFM interactions

“…We can also give some comparisons, at least, for the cases with spin-1/2 [22] and spin-1 [23] FM/AFM models; (i) With spin-1/2: No first-order phase transitions were exhibited, but the spin-3/2 model displays both the first-and second-order phase transitions. Therefore, the tricritical points and critical end points are also displayed.…”

The spin‐3/2 Ising model on a two‐layer Bethe lattice with AFM/AFM interactions

“…We should note that this is the only work with AFM/AFM interactions for spin-3/2 and thus we cannot provide any comparisons nor discussions, but we can at least give some comparison for the cases with the spin-1/2 AFM/AFM and FM/AFM models [35] and with the spin-3/2 FM/FM model [31]: no first-order phase transition was exhibited by the spin-1/2 models, but for the spin-3/2 model both first-order phase transitions and tricritical points are displayed; therefore, in this manner our results are model dependent. The re-entrant behavior was not observed for q = 3 and 4 in the spin-1/2 case but it was seen for all q values in the spin-3/2 case.…”

“…The behavior of the Ising thin films was studied through the use of layered Bethe lattices and Husimi trees [34]. The exact phase diagrams of spin-1/2 on a twolayer Bethe lattice with FM/AFM and AFM/AFM intralayer interactions were studied by using a pairwise approach [35]. Meanwhile, a Bethe lattice is an infinite Cayley or regular tree, i.e., a connected graph without circuits, and historically gets its name from the fact that its partition function is exactly that of an Ising model in the Bethe approximation [36].…”

The dynamic magnetic behaviors of the Blume–Capel Ising bilayer system

“…Research on magnetic bilayers has received much interest both from the experimental and theoretical point of view in recent years [1][2][3][4][5][6][7][8][9][10]. Experimentally, several works have been published on the properties of the magnetic bilayer such as FePt/Fe [11], FM/TbFe (FM=Fe, Py-permalloy, FeCo) [12], SiGe, SiC and GeC [13], Ni/Au [14], Fe/Ni and Fe/Co [15].…”

“…Experimentally, several works have been published on the properties of the magnetic bilayer such as FePt/Fe [11], FM/TbFe (FM=Fe, Py-permalloy, FeCo) [12], SiGe, SiC and GeC [13], Ni/Au [14], Fe/Ni and Fe/Co [15]. On the other hand, theoretically, the equilibrium behaviors of bilayer Ising systems consisting of single ions, namely spin-1/2, spin-1 etc., have been widely studied by utilizing the wellknown theoretical methods used in equilibrium statistical physics, such as the mean field theory (MFT) [16,17], the effective field theory (EFT) [18,19], the exact recursion equation on the Bethe lattice [6,7], the renormalization-group (RG) method [20,21], and Monte Carlo (MC) simulations [22,23].…”