  Antiferromagnets and quantum XY magnets in three space dimensions are
described by an effective Lagrangian that exhibits the same structure as the
effective Lagrangian of quantum chromodynamics with two light flavors. These
systems all share a spontaneously broken internal symmetry O($N$) $\to$
O($N$-1). Although the respective scales differ by many orders of magnitude,
the general structure of the low-temperature expansion of the partition
function is the same. In the nonabelian case, logarithmic terms of the form
$T^8 \ln T$ emerge at three-loop order, while for $N$=2 the series only
involves powers of $T^2$. The manifestation of the Goldstone boson interaction
in the pressure, order parameter, and susceptibility is explored in presence of
an external field.
