Existence of the 1/2 magnetization plateau in the S=1 Ising model with single-ion anisotropy on Z=3 Bethe lattice

By the simple updated infinite time-evolving block decimation (iTEBD) algorithm, the magnetization process and phase diagram of the antiferromagnetic and ferromagnetic spin-1 Ising model with single-ion anisotropy on the Z=3 Bethe lattice have been investigated. For the antiferromagnetic case, three magnetization plateaus, i.e., Mz=0, 1/2, and 1, are observed. The novel 1/2 plateau state, which was reported on the 1D spin chain previously, is shown to exist on the Z=3 Bethe lattice. For this classical model without any quantum fluctuations, the 1/2 magnetization plateau is suggested to be caused by the stability of spatially modulated spin structures. Furthermore, in the M z = 0 plateau, two different phases (an ideal Néel phase and an ideal large-D phase) are distinguished. The phase boundaries are determined exactly, and a rich phase diagram including four phases is obtained. In addition, the magnetization process of the ferromagnetic case is also discussed, but a relatively simple phase diagram without 1/2 plateau phase is determined. According to the energy level crossing, all the phase transitions in both cases are verified to be first-order ones.