Spatial distribution of Gaussian fluctuations of the molecular field and magnetization in the pyramid-like Ising nanoscopic system interacting with the substrate

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.