  We analyze the spontaneous rippling of graphene membranes as function of the
coupling between lattice deformations and electrons.
  We numerically study a model of an elastic membrane coupled to Dirac
fermions. We identify a phase transition from a flat to a rippled configuration
of the membrane when increasing the coupling and propose a scaling procedure
that allows us to effectively reach arbitrary large system sizes. We find that
the critical value of the coupling rapidly decays as the system increases its
size, in agreement with the experimental observation of an unavoidable stable
rippled state for suspended graphene membranes. This decay turns out to be
controlled by a power law with a critical exponent $\sim 1/2$.
