Abstract
Analytical solutions to nonlinear difference equations describing stationary states of the d -dimensional classical O(2) (XY) spin model are studied. The Hirota bilinear operator formalism is employed to obtain exact and approximate stationary vortexlike-mode solutions having a form somewhat similar to a discrete version of vortex solutions to the two-dimensional sine-Gordon equation. The former exists for a specific case, while the existence condition for the latter is much less restrictive. The obtained analytical result is demonstrated in numerical calculations of vortex profiles for a two-dimensional model O(2) spin system, in which a single vortex and a periodic array of vortex-antivortex pairs are shown.
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