Quantum critical scaling in magnetic field near the Dirac point in graphene

Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor f=1 in graphene, we discuss the scaling of the interaction-induced gaps in the vicinity of the Dirac point with the magnetic field. The gap at f=1 is shown to be bounded from above by E(1)/C, where E(n)=v_F√2nB is the Landau-level energy and C=5.985+O(1/N) is a universal number. The universal scaling functions are computed exactly for a large number of Dirac fermions N. We find a sublinear dependence of the gap at the laboratory fields of 10 T<B<50 T for realistic values of short-range repulsion between electrons, in quantitative agreement with observation.