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 eight 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 D=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. 
K. Essafi, J.-P. Kownacki, D. Mouhanna
cond-mat.stat-mech cond-mat.soft hep-th