  We consider the anisotropic quantum Heisenberg antiferromagnet (with
anisotropy $\lambda$) on a square lattice using a Chern-Simons (or
Wigner-Jordan) approach. We show that the Average Field Approximation (AFA)
yields a phase diagram with two phases: a Ne{\`e}l state for
$\lambda>\lambda_c$ and a flux phase for $\lambda<\lambda_c$ separated by a
second order transition at $\lambda_c<1$. We show that this phase diagram does
not describe the $XY$ regime of the antiferromagnet. Fluctuations around the
AFA induce relevant operators which yield the correct phase diagram. We find an
equivalence between the antiferromagnet and a relativistic field theory of two
self-interacting Dirac fermions coupled to a Chern-Simons gauge field. The
field theory has a phase diagram with the correct number of Goldstone modes in
each regime and a phase transition at a critical coupling $\lambda^* >
\lambda_c$. We identify this transition with the isotropic Heisenberg point. It
has a non-vanishing Ne{\` e}l order parameter, which drops to zero
discontinuously for $\lambda<\lambda^*$.
