The ensemble equivalence problem for Bose systems (nonideal Bose gas)

The problem of the equivalence of the canonical and grand canonical ensembles for nonideal Bose systems is considered for the example of three exactly solvable models, each of which undergoes a phase transition with the formation of a Bose condensate. It is shown that violation of the statistical (strong) equivalence of the ensembles is not a simple consequence of Bose condensation and equivalence is restored by changing the kind of the phase transition.