εexpansions for crumpled manifolds

To study properties of self-avoiding surfaces, we consider D-dimensional elastic manifolds embedded in d-dimensional space. In the (d,D) plane there is a line separating ideal (Gaussian), and self-avoiding (interacting) behaviors. We develop the techniques for systematic perturbation expansions, and renormalization-group analysis, about any point on this line. The usual {ε} expansion for polymers about d=4 is a special case. The exponents {ν} and {γ} are calculated to lowest order, providing very good values for polymers (D=1), and reasonable indications for surfaces (D=2).