  Finite size scaling for a first order phase transition where a continuous
symmetry is broken is developed using an approximation of Gaussian probability
distributions with a phenomenological "degeneracy" factor included. Predictions
are compared with data from Monte Carlo simulations of the three-dimensional,
XXZ Heisenberg antiferromagnet in a field in order to study the finite size
behavior on a $L \times L \times L$ simple cubic lattice for the first order
"spin-flop" transition between the Ising-like antiferromagnetic state and the
canted, XY-like state. Our theory predicts that for large linear dimension $L$
the field dependence of all moments of the order parameters as well as the
fourth-order cumulants exhibit universal intersections. Corrections to leading
order should scale as the inverse volume. The values of these intersections at
the spin-flop transition point can be expressed in terms of a factor $q$ that
characterizes the relative degeneracy of the ordered phases. Our theory yields
$q=\pi$, and we present numerical evidence that is compatible with this
prediction. The agreement between the theory and simulation implies a
heretofore unknown universality can be invoked for first order phase
transitions.
