Flat glassy phases and wrinkling of polymerized membranes with long-range disorder

We study polymerized membranes with long-range quenched internal disorder in the preferred metric and/or the extrinsic curvature characterized by disorder range exponents ${\mathit{z}}_{\mathrm{\mu }}$,${\mathit{z}}_{\mathrm{\kappa }}$, respectively. We find several new flat glassy phases stable at T>0 in different regions of the ${\mathit{z}}_{\mathrm{\mu }}$,${\mathit{z}}_{\mathrm{\kappa }}$ plane. We calculate the z-dependent roughness exponents and amplitudes that characterize these new phases. When ${\mathit{z}}_{\mathrm{\mu }}$,${\mathit{z}}_{\mathrm{\kappa }}$ exceed critical values ${\mathit{z}}_{\mathrm{\mu }}^{\mathit{c},}$${\mathit{z}}_{\mathrm{\kappa }}^{\mathit{c}}$ (characteristic of each phase), these glassy flat phases undergo a transition towards a crumpled phase, similar to the crumpled glass previously predicted.