Curvature disorder in tethered membranes: A new flat phase atT=0

We study the effect of quenched disorder on the behavior of tethered membranes. We consider D-dimensional membranes in a d-dimensional embedding space using expansions in {ε}=4-D and 1/d. Disorder is introduced via a random spontaneous curvature, such as would be caused by impurities that break the symmetry between the sides of the membrane, and via a random preferred metric. The presence of random spontaneous curvature is found to stiffen the long-wavelength bending rigidity, giving rise at temperature T=0 to a disordered flat phase associated with a new fixed point of the renormalization group. This phase is characterized by anomalous statistical and elastic properties similar to those found previously for pure membranes at T{≠}0, but due here to quenched disorder rather than thermal fluctuations.