Anqi Cheng, Anna Hasenfratz, Gregory Petropoulos, David Schaich
We show how to extract the scale-dependent mass anomalous dimension from the renormalization group invariant mode number of the massless Dirac operator. 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 investigate 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 can be controlled in practical lattice calculations. Our 12-flavor results indicate 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.
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http://arxiv.org/abs/1301.1355
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