Monte Carlo simulation of two-dimensional Shastry–Sutherland lattice has been carried out using heat-bath method. The dependencies of magnetization M on external field H have been obtained in the framework of classical Heisenberg model. In certain interval of exchange parameters ratio the plateau of magnetization corresponding to M = 1/3 has been observed. The influence of exchange anisotropy of “easy-axis” type on this plateau width is studied. It has been shown that even weak anisotropy (∼1−2%) leads to essential enlargement of the plateau. The dependence of critical temperature on exchange parameters ratio has been established.
The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.
Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m* = m/msat = 1/4, 1/3, and 1/2 (here msat is the saturation magnetization) exist even in the case of isotropic exchange interactions. The effect of exchange interaction on the width of the plateaus was studied. It was shown that depending on the ratio of exchange constants, there exist three regions corresponding to different types of the behavior of the system: the regions of a Neel-like antiferromagnet, a “dimer” antiferromagnet, and an intermediate region where the unique properties of Shastry–Sutherland lattices are most pronounced. The boundaries of these regions were also determined.
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