In the large d limit, D-dimensional tethered membranes with quenched randomnesses and with long range repulsive interactions 1/ryare studied. Due to the randomness in the metric, the flat phase is unstable and the spin-glass phase takes over. The phase diagram in the (y, D) plane is obtained. The crumpled phase is not affected by the randomness. The exact exponent for the radius of gyration in the spin-glass phase is given. The self-avoiding randomly polymerized membrane (d=3, D=2) is in the flat phase or in the crumpled glass phase. © 1994.
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