  The paper is devoted to the magnetic properties of isolated mesoscopic
grains. We demonstrate that under very general conditions the electron -
electron interactions in such grains can be taken into account by a simple
interaction Hamiltonian. This Hamiltonian involves only three coupling
constants which correspond to charging, exchange interaction, and
superconducting correlations. The most important condition for such a
description is that Thouless conductance of each grain is large. Under this
condition sample-to-sample fluctuations of the coupling constants can be
neglected. However, the thermodynamic properties can still remain
sample-specific due to the one-electron part of the Hamiltonian. If the grain
is made from a material which is close to the threshold of ferromagnetic
instability the mesoscopic fluctuations of the magnetization are especially
strong. Moreover, the situation becomes multi-stable: free energy of each grain
as a function of the magnetization is characterized by a large number of local
minima. We analyze the statistics of these minima and show that it possesses
simple scaling properties. Numerical simulations confirm this scaling.
