  The lowest-energy state of a macroscopic in which symmetry is spontaneously
broken, is a very stable wavepacket centered around a spontaneously chosen,
classical direction in symmetry space. However, for a Heisenberg ferromagnet
the quantum groundstate is exactly the classical groundstate. This coincides
with other exceptional properties of the ferromagnet, including spontaneous
time-reversal symmetry breaking, a reduced number of Nambu-Goldstone modes and
the absence of a thin spectrum (Anderson tower of states). Recent discoveries
of other non-relativistic systems with fewer Nambu-Goldstone modes suggest
these specialties apply there as well. I establish precise criteria for the
absence of quantum fluctuations and all the other features. In particular, it
is not sufficient that the order parameter commute with the Hamiltonian. It
leads to a measurably larger coherence time of superpositions in small but
macroscopic systems.
