2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230721Motivated 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 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) are the Landau level energies 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 magnetic fields for realistic values of short-range repulsion between electrons, and in quantitative agreement with observation.5 RevTex pages, 3 figures; added comments and references; cosmetic changes (this, published, version)Mesoscale and Nanoscale PhysicsStrongly Correlated Electronstext