Copolymer Networks and Stars: Scaling Exponents

We explore and calculate the rich scaling behavior of copolymer networks in solution by renormalization group methods. 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: The special convexity properties of the spectra allow for a multifractal interpretation while preserving stability of the theory. This behavior could not be found for power of field operators of usual $\phi^4$ field theory. 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. We furthermore provide a consistency check of two complementary renormalization schemes: epsilon expansion and renormalization at fixed dimension, calculating a large collection of independent exponents in both approaches.Comment: 30 pages, revtex, figures: 5 latex, 1 postscript. New Figs. Text improved. Citations adde

Multifractal dimension spectra in polymer physics

We study the multifractal properties of diffusion in the presence of an absorbing polymer and report the numerical values of the multifractal dimension spectra for the case of an absorbing self avoiding walk or random walk.Comment: 9 pages, latex, 3 latex picture