Fermion condensate
In a theory with two chiral fields, ψ
1 and ψ
2 with a global symmetry relating the relative phases of both fields, but at low temperatures, the correlation function is nonzero, then we say a
fermion condensate (also called chiral condensate) has formed. For example, in
QCD, there is an approximate (so there's no real
spontaneous symmetry breaking; the
VEV will always be aligned in a fixed direction) axial symmetry which is broken because the
quarks form a chiral condensate. See
Technicolor (physics) for another example.
BCS in
superconductivity is another.
To get a "feel" for chiral condensates, a good toy model to start with is the Schwinger model.