Abstract. Employs exact enumeration methods to study a number of configurational properties of self-avoiding random surfaces embedded in a three-dimensional simple cubic lattice. Self-avoiding surfaces are defined as a connected set of plaquettes in which no more than two plaquettes may meet along a common edge, and in which no plaquette can be occupied more than once. Based on enumerating surfaces containing up to 10 plaquettes, the author finds: (a) the number of n-plaquette surfaces, c_n, varies as mu ⁿn^{gamma -1}, with mu =13.2+or-0.2 and gamma =0.22+or-0.06, (b) the average number of perimeter edges of n-plaquette surfaces, (p_n), varies linearly with n, and (c) the mean-square radius of gyration of n-plaquette surfaces, (R_g²(n)), varies as n^{2 nu} , with 2 nu =1.075+or-0.05.

A corrigendum for this article has been published in 1986 J. Phys. A: Math. Gen. 19 3199

Print publication: Issue 12 (21 August 1985)