  We study thermodynamic properties of an Ising model of a ferromagnetic
nanoscopic pyramid deposited onto a ferromagnetic bulk substrate. The influence
of the interaction between the pyramid and the substrate is calculated in terms
of the equilibrium reduced-state (density) operator used for description of
thermodynamic properties of nanoscopic systems. The spatial distribution of the
fluctuations of molecular field and magnetization in the nanoscopic pyramid is
obtained in the Gaussian fluctuations approximation. Experimental consequences
for the magnetic force measurements are briefly discussed.
