  We use non-perturbative renormalization group techniques to calculate the
momentum dependence of thermal fluctuations of graphene, based on a
self-consistent calculation of the momentum dependent elastic constants of a
tethered membrane. We find a sharp crossover from the perturbative to the
anomalous regime, in excellent agreement with Monte Carlo results for graphene,
and give an accurate value for the crossover scale. Our work strongly supports
the notion that graphene is well described as a tethered membrane. Ripples
emerge naturally from our analysis.
