We study the non-perturbative behaviour of QED in a strong external
magnetic field using Rational Hybrid Monte Carlo (RHMC) simulations of lattice
QED. The RHMC method was developed for simulating lattice QCD. Previously we
showed that the magnetic field breaks chiral symmetry in the limit of zero bare
mass as had been predicted by Schwinger-Dyson methods. We are now simulating
at weaker magnetic fields to test that the chiral condensate scales as
$(eB)^{3/2}$ as predicted, where $B$ is the constant homogeneous external
magnetic field and $e$ is the electric charge. We first chose a much weaker
magnetic field. While we saw evidence that chiral symmetry was still broken,
it became clear that to measure the zero bare mass dependence of the chiral
condensate on $eB$ would require use of much larger lattices than we can
manage. We are therefore now performing simulations at a magnetic field with an
intermediate strength.