  We calculate the mesoscopic fluctuations of the magnetic anisotropy of
ferromagnetic nanoparticles. A microscopic spin-orbit Hamiltonian considered as
a perturbation of the much stronger exchange interaction first yields an
explicit expression for the anisotropy tensor. Then, assuming a simple random
matrix model for the spin-orbit coupling allows us to describe the fluctuation
of such a tensor. In the case of uniaxial anisotropy, we calculate the
distribution of the anisotropy constant for a given number of electrons, and
its variation upon increasing this number by one. The magnitude of the latter
is sufficient to account for the experimental data.
