The properties of one-dimensional spin-S (S⩾1) antiferromagnetic Ising chain with single-ion anisotropy

Magnetization plateaus in a doping finite Ising chain

“…For the 1D spin system with the translational symmetry of the ground state, Oshikawa et al have derived a necessary condition pðSÀmÞ ¼ integer for the occurrence of plateaus by employing a generalization of the Lieb-SchultzMattis theorem [15], where p is the spatial periodicity of the magnetic ground state, S is the magnitude of spin and m is the magnetization per site. Moreover, 2S þ1 magnetization plateaus have also been found in many theoretical studies, when the magnetic field increases from zero to its saturation values h s [16][17][18].…”

“…Thus the width of the intermediate plateaus is h s =J 1 Àh c =J 1 ¼ J 2 =J 1 S imp ÀS, increasing with the increase of quantum spin number of the impurity. For a homogeneous system with spin S, it has been verified that positive anisotropy is a necessary condition for the appearance of the 2S þ 1 plateaus [16]. Furthermore, magnetic anisotropy closely related with the spin-orbit coupling effects usually presents in realistic materials.…”

“…Meanwhile, some quasi-classical spin models using Ising spin instead of the Heisenberg operators also lead to the analogous pictures of magnetization plateaus. Particularly, those can be rigorously solved by analytical methods, such as the bound-alternating chains, decorated Ising chain and other quasi 1D models, which employ the transfer-matrix method, presenting us rich magnetization images for arbitrary finite temperature and arbitrary values of exchange coupling, the single-ion anisotropy and external magnetic field [6,7,16,22], as well as demonstrating the simplicity of transfer-matrix technique in dealing with the 1D classical models compared with those quantum means-bosonization technique, density matrix renormalization group method, field theory, etc.…”

Generalized Pauli principle for particles with distinguishable traits

“…Anghel's rules (5) are determinate when species are merged but some are indeterminate -even with amendments ( 16) -without implied assumptions or additional input when species are split [9][10][11].…”

The low temperature magnetic properties of the ferrimagnetic mixed spin Ising systems in the magnetic field

“…However, recently pure and mixed spin Ising systems in one dimension show the magnetic plateaus [15][16][17], i.e. quantization of the magnetization at the very low temperature or ground state of the system due to magnetic excitations, leading to the qualitatively same structures of the magnetization profiles of the Heisenberg and other systems.…”