Phase transition of the zeroth-kind for a weakly nonideal Bose gas (the Bogolubov model)

The system of interacting in pairs N bosons located on a three-dimensional torus with the sides L (length) is considered. The analysis of Hartree-Fock temperature equations shows that in Bogolubov model the properties of metastable states are similar to the properties of metastable states in the Maslov two-level model and Maslov strictly soluble model. And at critical temperature phase transition of the zeroth-kind occurs (that is, along with entropy jump the free energy is abruptly changed) and the metastable states disappear.