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How stable vortex-like magnetization in magnetic nanodisks with small aspectratio ($L/R<<1$) is affected by two antidots is investigated analytically andby Monte Carlo simulations. For suitable ranges of the physical parameters thisvortex presents bistable states when pinned around the antidots. The hysteresisloop obtained shows a central loop associated to the pinning mechanism of thevortex at the antidots. Our results agree qualitatively well with thoseprovided by experiments and micromagnetic simulations.Comment: 11 pages, 4 eps figures. Accepted in Journal of Applied Physic

Analytical and Monte Carlo study of two antidots in magnetic nanodisks with vortex-like magnetization