  Spontaneous symmetry breaking (SSB) is a widespread phenomenon in several
areas of physics. In this paper I wish to illustrate some situations where
spontaneous symmetry breaking presents non obvious aspects. The first example
is taken from molecular physics and is related to the paradox of existence of
chiral molecules. The second case refers to a Dirac field in presence of a
magnetic field. Gusynin, Miransky and Shovkovy have shown that
Nambu-Jona-Lasinio (NJL) models, where SSB of chiral symmetry takes place for
the nonlinear coupling over a certain threshold, in presence of a magnetic
field exhibit SSB for any value of the coupling. They called this phenomenon
magnetic catalysis. I will discuss this problem in 2 + 1 dimensions from an
operatorial point of view and show that the basic phenomenon is a double
pairing induced by the magnetic field in the vacuum for any value of the mass.
This pairing provides the environment responsible for chiral symmetry breaking
in NJL models with very weak nonlinearities. The third case illustrates briefly
SSB in stationary nonequilibrium states and its possible relevance in natural
phenomena.
