B dependence of the QED chiral condensate induced by an external magnetic field.

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.