Statistical mechanics of randomly polymerized membranes.

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