  Antiferromagnets and ferromagnets are archetypes of the two distinct (type-A
and type-B) ways of spontaneously breaking a continuous symmetry. Although
type-B Nambu--Goldstone modes arise in various systems, the ferromagnet was
considered pathological due to the stability and symmetry-breaking nature of
its exact ground state. However, here we show that symmetry-breaking in
ferrimagnets closely resembles the ferromagnet. In particular, there is an
extensive ground state degeneracy, there is no Anderson tower of states, and
the maximally polarized ground state is thermodynamically stable. Our results
are derived analytically for the Lieb--Mattis ferrimagnet and numerically for
the Heisenberg ferrimagnet. We argue that these properties are generic for
type-B symmetry-broken systems, where the order parameter operator is a
symmetry generator.
