Stability of QED
  It is shown for a class of random, time-independent, square-integrable, three-dimensional magnetic fields that the one-loop effective fermion action of four-dimensional QED increases faster than a quadratic in B in the strong coupling limit. The limit is universal. The result relies on the paramagnetism of charged spin - 1/2 fermions and the diamagnetism of charged scalar bosons. 
M. P. Fry
hep-th hep-lat hep-ph