  We study the statistical mechanics of binary systems under gravitational
interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional
space. Considering the binary systems, in the microcanonical and canonical
ensembles, we show that in the microcanonical systems, unlike the Newtonian
gravity, there is a sharp phase transition, with a high-temperature homogeneous
phase and a low temperature clumped binary one. Defining an order parameter in
the canonical systems, we find a smoother phase transition and identify the
corresponding critical temperature in terms of physical parameters of the
binary system. Our results for the binary system provide a hint to understand
the phase transitions in the N-body system by considering it as a constituent
of binary subsystems.
