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

Abstract

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 $\gamma_m=0.25$.