Wrinkling transition in quenched disordered membranes at two loops

We investigate the flat phase of quenched disordered polymerized membranes by means a two-loop, weak-coupling computation performed near their upper critical dimension ${D}_{uc}=4$, generalizing one-loop Morse et al. [D. C. al., Phys. Rev. A 45, R2151 (1992); D. and T. Lubensky, 46, 1751 (1992)]. Our work confirms existence finite-temperature, finite-disorder wrinkling transition, which has been recently identified Coquand [O. E 97, 030102(R) (2018)] using nonperturbative renormalization group approach. also point out ambiguities in two-loop that prevent exact identification properties novel fixed associated with very likely requires three-loop order