Condensed Matter Physics, 1997, No 10, p. 9-40, English
DOI:10.5488/CMP.10.9
Title: STATISTICS OF MULTICOMPONENT POLYMER STARS
Authors: C. von Ferber (Fachbereich Physik, Universitat Essen,
D-45117 Essen,
Germany; School of Physics and Astronomy, Tel Aviv University, IL-69978
Tel-Aviv, Israel), Yu. Holovatch (Institute for Condensed Matter Physics of
the Ukrainian Academy of Sciences, 1 Svientsitskii St., UA 290011 Lviv-11,
Ukraine)
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.