  One of the most exciting phenomena observed in crystalline disordered
membranes, including a suspended graphene, is rippling, i.e. a formation of
static flexural deformations. Despite an active research, it still remains
unclear whether the rippled phase exists in the thermodynamic limit, or it is
destroyed by thermal fluctuations. We demonstrate that a sufficiently strong
short-range disorder stabilizes ripples, whereas in the case of a weak disorder
the thermal flexural fluctuations dominate in the thermodynamic limit. The
phase diagram of the disordered suspended graphene contains two separatrices:
the crumpling transition line dividing the flat and crumpled phases and the
rippling transition line demarking the rippled and clean phases. At the
intersection of the separatrices there is the unstable, multicritical point
which splits up all four phases. Most remarkably, rippled and clean flat phases
are described by a single stable fixed point which belongs to the rippling
transition line. Coexistence of two flat phases in the single point is possible
due to non-analiticity in corresponding renormalization group equations and
reflects non-commutativity of limits of vanishing thermal and rippling
fluctuations.
