Two-loop renormalization group analysis of 2D Dirac fermion with random mass

We perform a two-loop renormalization group analysis for Dirac fermions with random mass in 2-epsilon dimensions. In two dimensions, the random mass is marginally irrelevant at the clean-limit fixed point, but in the two-loop analysis we find an IR unstable fixed point at a finite disorder strength. Using the epsilon expansion [1,2,3], we evaluate the localization length exponent, the dynamical exponent, and the scaling dimension of the (uniform) mass term at the IR unstable fixed point. We compare our results with earlier 3-loop [4] and 4-loop [5] calculations for the massless Gross-Neveu model.


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