Copolymer networks: the spectrum of scaling dimensions

We explore the intersection properties of stars of random and self-avoiding walks. We show how the corresponding scaling exponents govern the scaling behavior of copolymer networks in solution. We derive and calculate these exponents from a renormalization group analysis of a corresponding Edwards Hamiltonian. Our third-order spectrum of exponents calculated by field-theoretic renormalization shows remarkable features: All exponents are scaling dimensions of composite power of field operators, convexity of the spectrum allows for a multifractal interpretation, and the 2D limit has no simple Kac formula like structure.