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We define a scale-dependent effective mass anomalous dimension from thescaling of the mode number of the massless Dirac operator, which connects theperturbative $\gamma_m$ of an asymptotically-free system to the universal$\gamma_m^{\star}$ at a conformal fixed point. We use a stochastic algorithm tomeasure the mode number up to the cutoff scale on lattices as large as $48^4$.Focusing on SU(3) lattice gauge theory with $N_f = 12$ massless fundamentalfermions, we examine systematic effects due to finite volumes and non-zerofermion masses. Our results suggest the existence of an infrared fixed pointwith $\gamma_m^{\star} \approx 0.25$. Our method provides a unique probe tostudy systems from the UV to the IR. It is universal and can be applied to anylattice model of interest, including both chirally-broken and IR-conformalsystems.

Determining the mass anomalous dimension through the eigenmodes of Dirac operator