Using very precise measurements of the critical couplings for the chir
al 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. Co
ntrary 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. Trivi
ality a la Nambu-Jona Lasinio is also ruled out.