  The development and applications of the method of quasiaverages developed by
N. N. Bogoliubov to quantum statistical physics and to quantum solid state
theory and, in particular, to quantum theory of magnetism, were analyzed. The
problem of finding the ferromagnetic, antiferromagnetic and superconducting
symmetry broken solutions of the correlated lattice fermion models was
discussed within the irreducible Green functions method. A unified scheme for
the construction of generalized mean fields (elastic scattering corrections)
and self-energy (inelastic scattering) in terms of the Dyson equation was
generalized in order to include the source fields. The interrelation of the
Bogoliubov's idea of quasiaverages and the concepts of symmetry breaking and
quantum protectorate was discussed briefly in the context of quantum
statistical physics. The idea of quantum protectorate reveals the essential
difference in the behaviour of the complex many-body systems at the low-energy
and high-energy scales. It was shown that the role of symmetry (and the
breaking of symmetries) in combination with the degeneracy of the system was
reanalyzed and essentially clarified within the framework of the method of
quasiaverages. The complementary notion of quantum protectorate might provide
distinctive signatures and good criteria for a hierarchy of energy scales and
the appropriate emergent behavior.
