Crumpled-to-flat transition of quenched disordered membranes at two-loop order

We investigate the effects of quenched elastic disorder on the nature of the crumpling-to-flat transition of D-dimensional polymerized membranes using a two-loop computation near the upper critical dimension Dc=4. While the pure system undergoes fluctuation-induced first order transitions below Dc and for an embedding dimension d<dc,pure 218.2, one observes, in presence of disorder, the emergence of various regions of second order governed by a disordered stable fixed point for d<dc1~ dc,pure. This opens the possibility of a new universality class associated with the crumpling-to-flat transition of disordered membranes in $d=3$