  The ground state energy and the singlet-triplet energy gap of the
antiferromagnetic Heisenberg model on a ladder is investigated using a mean
field theory and the density matrix renormalization group. Spin wave theory
shows that the corrections to the local magnetization are infinite. This
indicates that no long range order occurs in this system. A flux-phase state is
used to calculate the energy gap as a function of the transverse coupling,
$J_\perp$, in the ladder. It is found that the gap is linear in $J_\perp$ for
$J_\perp\gg 1$ and goes to zero for $J_\perp\to 0$. The mean field theory
agrees well with the numerical results.
