Copolymer Networks and Stars: Scaling Exponents

Details Copolymer Networks and Stars: Scaling Exponents Copolymer Networks and Stars: Scaling Exponents

1997-05-27

arxiv.org/abs/cond-mat/9705278v2

Phys. Rev. E 56 (1997) 6370

Physics

Condensed Matter

Soft Condensed Matter

30 pages, revtex, figures: 5 latex, 1 postscript. New Figs. Text improved. Citations added

Scientific paper

10.1103/PhysRevE.56.6370

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.

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