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}≃218.2, one observes, in the presence of disorder, the emergence of various regions of second order governed by a disordered stable fixed point for d<d_{c1}∼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.