Two- and three-dimensional copolymer stars and multifractality
by C. von Ferber
Abstract: Abstract: We compare perturbative expansions of the Edwards model, lattice
Monte Carlo simulations, and exact results using conformal invariance
and 2D quantum gravity for the (scaling) properties of random walks
with self and/or mutual avoidance interactions. We are especially
interested in the question of the universality of the problem of self
and mutually avoiding walks in two and three dimensions, as well as in
validating multifractality found in these situations by field theoretic
methods based on the Edwards model and by a conformal theory in 2D.
We focus on model star copolymers in two dimensions: walks or polymers
of different species described by either random walks (RW) or
self-avoiding walks (SAW) with a common starting point; the species
avoid each other mutually.
In our field thoretic approach we mapped the problem of finding the
scaling properties of the copolymer star to that of determining the
anomalous dimensions of appropriate local field operator products.
Resummation of the perturbation series recently extended to 4th order
provides reliable numeric values for a family of exponents that
displays multifractal behavior.
These results have implications on the scaling of branched polymeric
systems, the effective mutual interaction of star polymers, and
For More Information: Iwan Jensen tel. 03 8344-5214 email: email@example.com