Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 25: Symposium Renormalization and Scaling (SYRS) – Contributed Talks II
DY 25.2: Vortrag
Samstag, 5. März 2005, 16:15–16:30, TU H3010
Star polymer scaling - 4th order RG results and applications — •Christian von Ferber1, Yurij Holovatch2,3, Verena Schulte-Frohlinde1 und Alexander Blumen1 — 1Theoretische Polymerphysik, Universität Freiburg — 2Institute for Condensed Matter Physics and Ivan Franko National University of Lviv, Ukraine — 3Johannes Kepler Universität Linz, Austria
The overall scaling properties of a branched polymeric structure in
solution can be derived in terms of the scaling behavior of the
star-like branching units that define its local topology. Various
physical processes and situations are governed by these: the mean
force between two star polymers, the correlations of the brancing
units in a star burst dendrimer, the denaturation process of DNA
double strands as well as trapping processes involving traps aligned
on a polymer where the random walk of each trapped particle describes
a branch with branching point at the trap. More complex multifractal
behavior occurs in the latter example where the branches
differ. In a field thoretic approach we map the problem
of finding the scaling properties of the star-like branching unit to
that of determinig the anomalous dimensions of an appropriate local
field operator product. We present recent 4th order RG results
obtained in the minimal subtraction scheme of the є=4−d
expansion. We compare our results to previous 3rd order є-
and fixed dimension expansions as well as to exact results in
2D and MC simulations.
[1]V. Schulte-Frohlinde, Yu. Holovatch, C. von Ferber, A. Blumen. Phys. Lett. A 328:335-340 (2004).
[2]C. von Ferber, Yu. Holovatch, ed. Condens. Matt. Phys. 5(2002).