  Consider a $d$-dimensional antiferromagnet with a quantum disordered ground
state and a gap to bosonic excitations with non-zero spin. In a finite external
magnetic field, this antiferromagnet will undergo a phase transition to a
ground state with non-zero magnetization, describable as the condensation of a
dilute gas of bosons. The finite temperature properties of the Bose gas in the
vicinity of this transition are argued to obey a hypothesis of ZERO
SCALE-FACTOR UNIVERSALITY for $d < 2$, with logarithmic violations in $d=2$.
Scaling properties of various experimental observables are computed in an
expansion in $\epsilon=2-d$, and exactly in $d=1$.
