  The object of this study is a cell model with Curie-Weiss interaction
potential. We have already proved the possibility of a mathematically rigorous
transition from a continuous system of interacting particles to such a model
and made an accurate calculation of its grand partition function. In the
present research, we derive an explicit accurate equation of state of the cell
model with Curie-Weiss potential. It turned out that this model has a sequence
of first-order phase transitions at temperatures below the critical. We
analyzed the mechanism of these transitions based on the behavior of the
chemical potential as a function of density. Thus we found the points of phase
coexistence without going beyond the microscopic approach. We also proposed a
mathematically strict definition of the critical temperature as a function of
the microscopic parameters of the model. We determined the parameters of the
critical points and plotted phase diagrams which cover the area of the first
three phase transitions in the sequence.
