Volume 39, Number 1, July I 1997
|Page(s)||31 - 36|
|Section||Condensed matter: structure, thermal and mechanical properties|
|Published online||01 September 2002|
Copolymer networks: Multifractal dimension spectra in polymer field theory
Fachbereich Physik, Universität Essen -
D-45117 Essen, Germany
2 School of Physics and Astronomy, Tel Aviv University - IL-69978 Tel-Aviv, Israel
3 Institute for Condensed Matter Physics, Ukrainian Academy of Sciences, UA-290011 Lviv, Ukraine
Accepted: 25 May 1997
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 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.
PACS: 61.41.+e – Polymers, elastomers, and plastics / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Fr – Equilibrium properties near critical points, critical exponents
© EDP Sciences, 1997
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