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We investigate the flat phase of $D$-dimensional crystalline membranesembedded in a $d$-dimensional space and submitted to both metric and curvaturequenched disorders using a nonperturbative renormalization group approach. Weidentify a second order phase transition controlled by a finite-temperature,finite-disorder fixed point unreachable within the leading order of$\epsilon=4-D$ and $1/d$ expansions. This critical point divides the flowdiagram into two basins of attraction: that associated to thefinite-temperature fixed point controlling the long distance behaviour ofdisorder-free membranes and that associated to the zero-temperature,finite-disorder fixed point. Our work thus strongly suggests the existence of awhole low-temperature glassy phase for quenched disordered graphene,graphene-like compounds and, more generally, crystalline membranes.

A glassy phase in quenched disordered graphene and crystalline membranes