  We investigate the eigenmodes of the massless Dirac operator to extract the
scale-dependent fermion mass anomalous dimension gamma_m(mu). By combining
simulations on multiple lattice volumes, and when possible several gauge
couplings, we are able to measure the anomalous dimension across a wide range
of energy scales. The method that we present is universal and can be applied to
any lattice model of interest, including both conformal or chirally broken
systems. We consider SU(3) lattice gauge theories with Nf=4, 8 and 12 light or
massless fermions. The 4-flavor model behaves as expected for a QCD-like system
and demonstrates that systematic effects are manageable in practical lattice
calculations. Our 12-flavor results are consistent with the existence of an
infrared fixed point, at which we predict the scheme-independent mass anomalous
dimension gamma_m^*=0.32(3). For the 8-flavor model we observe a large
anomalous dimension across a wide range of energy scales. Further investigation
is required to determine whether Nf=8 is chirally broken and walking, or if it
possesses a strongly-coupled conformal fixed point.
