  We present theoretical results for the equilibrium Josephson current through
an Anderson dot tuned into the magnetic regime, using Hirsch-Fye Monte Carlo
simulations covering the complete crossover from Kondo-dominated physics to
$\pi$ junction behavior in a numerically exact way. Within the `magnetic'
regime, $U/\Gamma\gg 1$ and $\epsilon_0/\Gamma\leq 1$, the Josephson current is
found to depend only on $\Delta/T_K$, where $\Delta$ is the BCS gap and $T_K$
the Kondo temperature. The junction behavior can be classified into four
different quantum phases. We describe these behaviors, specify the associated
three transition points, and identify a local minimum in the critical current
of the junction as a function of $\Delta/T_K$.
