  The energy of a displaced magnetic vortex in a cylindrical particle made of
isotropic ferromagnetic material (magnetic dot) is calculated taking into
account the magnetic dipolar and the exchange interactions. Under the
simplifying assumption of small dot thickness the closed-form expressions for
the dot energy is written in a non-perturbative way as a function of the
coordinate of the vortex center. Then, the process of losing the stability of
the vortex under the influence of the externally applied magnetic field is
considered. The field destabilizing the vortex as well as the field when the
vortex energy is equal to the energy of a uniformly magnetized state are
calculated and presented as a function of dot geometry. The results (containing
no adjustable parameters) are compared to the recent experiment and are in good
agreement.
