ε-Expansion for Self-Avoiding Tethered Surfaces of Fractional Dimension

The equilibrium statistics of self-avoiding Euclidean surfaces of fractional dimension D and fixed connectivity in a d -dimensional space is investigated. An ε = 4 D - d (2 - D ) expansion about the upper critical curve d = 4 D /(2 - D ) is developed by generalizing the direct renormalization treatment of polymers ( D = 1). The exponents ν and γ are computed to O (ε). There are O (ε) corrections to γ only for D near an integer.