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Finite size scaling is a powerful tool to study the critical properties ofsystems governed by one relevant operator, assuming all irrelevant operatorshave scaling dimensions much smaller then zero. This condition is likely notsatisfied in many-fermion conformal systems where perturbation theory predictsa nearly-marginal irrelevant gauge coupling. In this work we carry out a newinvestigation of SU(3) lattice gauge theory with 12 fundamental flavors.Analyzing data at many different gauge couplings, our preliminary resultsindicate that a finite size scaling analysis that takes into account the effectof a nearly-marginal gauge coupling can resolve many of the inconsistenciesobserved previously in this system, leading to results consistent withconformal infrared dynamics and predicting a mass scaling anomalous around$\gamma_m=0.25$.

Finite size scaling and the effect of the gauge coupling in 12 flavor systems