Mesoscopic magnetization fluctuations for metallic grains close to the Stoner instability

This 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-salnple 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 that is close to the threshold of ferromagnetic instability, the mesoscopic fluctuations of the magnetization are especially strong. Moreover, the situation becomes multistable: 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.