Weak self-avoidance and crumpling in random surfaces with extrinsic curvature

We introduce an explicit local self-avoidance in both fixed and dynamically triangulated random surfaces with a gaussian (Polyakov) plus extrinsic curvature action in the hope that this might approximate a superstring model. We look at the effect this has on the crumpling transitions exhibited by the surfaces embedded in three dimensions and contrast the results with those obtained in simulations of self-avoiding tethered and fluid membranes in the context of solid state physics.