  A microscopic Hamiltonian of the magnetostatic interaction is discussed. This
long-range interaction can play an important role in mesoscopic systems leading
to an ordered ground state.
  The self-consistent mean field approximation of the magnetostatic interaction
is performed to give an effective Hamiltonian from which the spontaneous,
self-sustaining currents can be obtained.
  To go beyond the mean field approximation the mean square fluctuation of the
total momentum is calculated and its influence on self-sustaining currents in
mesoscopic cylinders with quasi-1D and quasi-2D conduction is considered. Then,
by the use of the microscopic Hamiltonian of the magnetostatic interaction for
a set of stacked rings, the problem of long-range order is discussed. The
temperature $T^{*}$ below which the system is in an ordered state is
determined.
