The effect of quenched random internal disorder on tethered membranes is studied by modifying treatments of pure systems to allow for small local fluctuations in the metric due to defects. To lowest order in ε=4-D, where D is the internal membrane dimensionality, we find that the flat pure phase is stable to disorder at finite temperatures, but unstable at low temperatures to a phase that lies outside the range of the ε expansion. For D<4 the instability is triggered by any finite amount of disorder, while for D>4 there is a threshold value of disorder below which the flat phase is stable at all temperatures. We speculate on the nature of the new phase. We argue that the low-temperature instability persists in the presence of random spontaneous curvature, and show that the flat phase is always unstable when unbound disclinations are included in the disorder.

• Received 5 April 1991

DOI:https://doi.org/10.1103/PhysRevA.44.3525