  Finite size scaling is a powerful tool to study the critical properties of
systems governed by one relevant operator, assuming all irrelevant operators
have scaling dimensions much smaller then zero. This condition is likely not
satisfied in many-fermion conformal systems where perturbation theory predicts
a nearly-marginal irrelevant gauge coupling. In this work we carry out a new
investigation of SU(3) lattice gauge theory with 12 fundamental flavors.
Analyzing data at many different gauge couplings, our preliminary results
indicate that a finite size scaling analysis that takes into account the effect
of a nearly-marginal gauge coupling can resolve many of the inconsistencies
observed previously in this system, leading to results consistent with
conformal infrared dynamics and predicting a mass scaling anomalous around
$\gamma_m=0.25$.
