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 $D_c=4$. While the pure system undergoes fluctuation-induced first order transitions below $D_c$ and for an embedding dimension $d<d_{c,pure}\simeq 218.2$, one observes, in presence of disorder, the emergence of various regions of second order governed by a disordered stable fixed point for $d<d_{c1}\sim d_{c,pure}$. This opens the possibility of a new universality class associated with the crumpling-to-flat transition of disordered membranes in $d=3$