  Polymerized phantom membranes are revisited using a nonperturbative
renormalization group approach. This allows one to investigate both the
crumpling transition and the low-temperature, flat, phase in any internal
dimension D and embedding dimension d, and to determine the lower critical
dimension. The crumpling phase transition for physical membranes is found to be
of second order within our approximation. A weak first-order behavior, as
observed in recent Monte Carlo simulations, is however not excluded.
