Generalizedεexpansion for self-avoiding tethered manifolds

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Abstract
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 ν 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,D→0 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.

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