Testing logarithmic violations to scaling in strongly coupled QED

Using very precise measurements of the critical couplings for the chiral transition of non-compact QED_4 in 10^4, 12^4 and 14^4 lattices we analyse the behaviour of the order parameter at the critical point using the equation of state of a logarithmically improved scalar mean field theory, that of the Nambu-Jona Lasinio theory and a pure power law. The first case is definitively excluded by the numerical data. Contrary to that, very high quality fits can be found for the other two cases. A more complex analysis including the susceptibility is however able to clearly distinguish between the last two possibilities. Triviality a la Nambu-Jona Lasinio is also ruled out.