GENERALIZED EPSILON-EXPANSION FOR SELF-AVOIDING TETHERED MANIFOLDS

We present a scheme of interpreting the generalized ε expansion encountered in the renormalization-group analysis of D-dimensional self-avoiding tethered manifolds embedded in d-dimensional external space. Owing to the nonlinear nature of the parameter ε, O(ε) results of previous studies of the ε expansion are somewhat ambiguous. Our scheme resolves ambiguities and gives optimal numerical results to every order in ε. The O(ε) optimal values of the radius-of-gyration exponent are calculated for polymers in two and three dimensions, and for membranes in various dimensions. The optimized polymer exponents are better than the O(ε) results obtained from the traditional ε expansion. The exponent for two-dimensional membranes embedded in high-dimensional space, i.e., for D=2 and d, is 4/d in agreement with the Flory exponent. We further explore the ε-expansion properties in the limit d,D0 and find multiple-body excluded-volume interactions to be relevant. We show that these interactions cannot be ignored in the physically relevant case of two-dimensional membranes in three-dimensions. © 1990 The American Physical Society.