Anomalous thermodynamics of coulomb-interacting massless dirac fermions in two spatial dimensions

It is argued that the specific heat of N massless Dirac fermions in two spatial dimensions interacting with 1/r Coulomb interactions is suppressed logarithmically relative to its noninteracting counterpart. The (dimensionless) coefficient of the logarithm is calculated in a closed form in the leading order in large N expansion, but to all orders in the effective fine structure constant, αF, a procedure which takes into account finite temperature screening. This effect is expected to occur in a single-layer graphene embedded in a dielectric medium. Its dependence on the dielectric constant is calculated analytically.