Abstract
The properties of the two-dimensional antiferromagnet of spin 1/2 on a square lattice with nearest- and next-nearest-neighbors interactions in a strong magnetic field close to saturation are studied in terms of the equivalent Bose-gas problem. A phase with a gap in the elementary excitations spectrum, short-range-ordered ground state, and a corresponding plateau in the magnetization curve is shown to exist in the interval of fields between the first and second critical fields ${\mathit{h}}_{0}$h${\mathit{h}}_{01}$. Its existence is closely related to the two-particle attraction in the vicinity of the wave vector ${\mathbf{p}}_{0\mathit{u}}$=(\ensuremath{\pi},\ensuremath{\pi}). In the interval between the second and third critical fields ${\mathit{h}}_{01}$h${\mathit{h}}_{\mathit{c}\mathit{f}}$ the system behaves as a quasi-one-dimensional magnetic phase with long-range order in the ground state and a gapless mode. The magnetization depends on field linearly, with logarithmic corrections.
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