First-order phase transitions in polymerized phantom membranes.

The crumpled-to-flat phase transition that occurs in D-dimensional polymerized phantom membranes embedded in a d-dimensional space is investigated nonperturbatively using a field expansion up to order 8 in powers of the order parameter. We get the critical dimension dcr(D) that separates a second-order region from a first-order one everywhere between D=4 and 2. Our approach strongly suggests that the phase transitions that take place in physical membranes are of first order in agreement with most recent numerical simulations.