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The mode number of the Dirac operator scales with an exponent related to themass anomalous dimension gamma_m. This relation holds both in IR-conformalsystems, as well as in confining systems for large enough eigenvalues. Weinvestigate the Nf=4, 8 and 12 flavor SU(3) systems at several couplings nearthe chiral limit, and show that in general the scaling exponent varies with theeigenvalue, describing the dependence of gamma_m on the energy (or,equivalently, on the running coupling). This energy dependence can be exploredeven with fixed lattice parameters (bare coupling and mass). We find that forthe 4 flavor system the mass anomalous dimension decreases as the energyincreases, consistent with perturbative expectations. For the 8 flavor systemthe energy dependence is too weak to be observable at present. The 12 flavorsystem at our strongest couplings shows the anomalous dimension increasing withenergy, consistent with backward flow and the presence of an infrared fixedpoint. At weaker couplings we determine a preliminary value for the massanomalous dimension of the 12 flavor system at the infrared fixed point,gamma_m^*=0.27(3).

Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems