Condensed Matter Physics, 1997, No 10, p. 9-40, English
We analyze a polymer network made of chemically different polymer species. Considering the star-like vertices constituting it in order to describe their scaling properties we introduce a new set of critical exponents. In the case of network made of two species of polymers we call them copolymer star exponents. By means of mapping our theory on appropriate Lagrangean field theory we calculate these exponents as well as the exponents governing scaling properties of star of mutually avoiding walks in the third order of perturbation theory. In the case of homogeneous stars we recover previously obtained values of star exponents. Our results agree as well with the previous studies of special cases which were done to the second order of the \epsilon-expansion. We found consistency and stability of the results in d=2 and d=3 with expected growing of deviations for large number of arms of one star. The same methods were applied previously to the problem of uniform star polymers and have led to results in good agreement with Monte Carlo simulations. We hope our present calculations might also stimulate Monte Carlo studies of the copolymer star problem. The resummed values of the exponents for stars of mutually avoiding walks are in fair agreement with an exact result previously conjectured at d=2. The study performed for d=2 could give some insight to the problem of mapping our theory to a two dimensional conformal field theory. By studying the convexity properties of the spectrum of copolymer star exponents we show that they are a good candidate for finding application in the theory of multifractal spectra generated by the harmonic diffusion near the absorbing fractal.Comments: Figs. 6, Refs. 61, Tabs. 11.
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