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By molecular-dynamics simulation, we investigate the possible existence of a crumpling transition for a model of tethered membranes, where the particles are tethered by a continuous potential. For distantneighbor interactions, the potential is repulsive and contains a variable hard-core diameter parameter. By varying this parameter, we are able to study in detail the effect of self-avoidance. Our results suggest the interpretation that self-avoiding two-dimensional tethered membranes are asymptotically flat, even without an explicit bending rigidity, and that there is no crumpling transition except for "phantom" membranes.PACS numbers: 64.60.-i, 82.65.-i In recent years there has been considerable interest in the large-scale properties of random surfaces in the context of both field theory x and condensed-matter theory. 2 Condensed-matter systems in which surfaces and interfaces play a significant role include microemulsions, lipid bilayers, vesicles, and suspensions of monolayers of exfoliated layered crystals. While much of the statistical mechanics of two-dimensional surfaces embedded in a higher-dimensional space remains to be understood, it is known that there is no single universality class which encompasses all such systems. 3 Recently, Kantor, Kardar, and Nelson 4 introduced an interesting model of random surfaces, namely, the tethered membrane. In this model, particles (hard spheres of diameter

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