  We explore the rich scaling behavior of copolymer networks in solution. We
establish a field theoretic description in terms of composite operators. Our
3rd order resummation of the spectrum of scaling dimensions brings about
remarkable features: Convexity of the spectra allows for a multifractal
interpretation. This has not been conceived for power of field operators of
$\phi^4$ field theory before. The 2D limit of the mutually avoiding walk star
apparently corresponds to results of a conformal Kac series. Such a
classification seems not possible for the 2D limit of other copolymer stars.
The 3rd order calculation of a large collection of exponents furthermore allows
for a consistency check of two complementary schemes: epsilon expansion and
renormalization at fixed dimension.
