  By adding a small, irrelevant four fermi interaction to the action of
noncompact lattice Quantum Electrodynamics (QED), the theory can be simulated
with massless quarks in a vacuum free of lattice monopoles. The lattice theory
possesses a second order chiral phase transition which we show is
logarithmically trivial, with the same systematics as the Nambu-Jona Lasinio
model. The irrelevance of the four fermi coupling is established numerically.
The widths of the scaling windows are examined in both the coupling constant
and bare fermion mass directions in parameter space. For vanishing fermion mass
we find a broad scaling window in coupling. By adding a small bare fermion mass
to the action we find that the width of the scaling window in the fermion mass
direction is very narrow. Only when a subdominant scaling term is added to the
leading term of the equation of state are adequate fits to the data possible.
The failure of past studies of lattice QED to produce equation of state fits
with adequate confidence levels to seriously address the question of triviality
is explained. The vacuum state of the lattice model is probed for topological
excitations, such as lattice Monopoles and Dirac strings, and these objects are
shown to be non-critical along the chiral transition line as long as the four
fermi coupling is nonzero.
