Magnetic phase transition of the first kind in a system of spherical nanoclusters with the point dipole

The possibility of phase transition of the first kind in a system of free single-domain magnetic clusters is considered. To determine the domain of the system parameters where the phase transtion of the first kind (the domain of stability loss of the homogeneous distribution of the system) is possible, an equation of state of a system consisting of solid spheres of the diameter d containing the point dipole with the moment μ is constructed. It is shown that, taking into account the dipole-dipole interactions, given with accuracy up to the quadratic term in the expansion with respect to (1/kT) in the expression for the second virial coefficient, the equation of state of the system is the Berthelot equation. The value of the critical temperature and the condition under which the phase transition of the first kind (the coexistence of the liquid and gas phases) is possible in the system are determined as functions of the system parameters: the size of the clusters, their dipole moment, and the temperature of the system.