Magnetic properties of two-dimensional random systems of Ising dipoles

Abstract Within the framework of the generalized mean-field theory, two-dimensional random systems of point Ising magnetic dipoles of both fluid and lattice type are considered. In the former case, the precise expression for the distribution function of random magnetic fields is found, the impossibility of ferromagnetic ordering established and the susceptibility of the system in a paramagnetic state is calculated. In the latter case, it has been shown that the ground state of the system of Ising dipoles placed in randomly filled sites of two-dimensional square lattice, depends on the fraction p of the filled sites: at p > p c =0.63, the system is ferromagnetic, otherwise—paramagnetic. The transition between those states is of percolation nature. Temperature dependencies of the magnetization in the ferromagnetic phase and susceptibility of the system in the paramagnetic phase have been found.