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.

• Received 10 November 2008

DOI:https://doi.org/10.1103/PhysRevE.79.040101