Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Polymers in Disordered Media - the shortest, the longest and the
  mean(est) SAW on percolation clusters   Long linear polymers in strongly disordered media are well described by
self-avoiding walks (SAWs) on percolation clusters. The length-distribution of
these SAWs encompasses to distinct averages, viz. the averages over cluster-
and SAW-conformations. For the latter average, there are two basic options, one
being static and one being kinetic. It is well known for static averaging that
if the disorder of the underlying medium is weak, differences to the ordered
case appear merely in non-universal quantities. Using dynamical field theory,
we show that the same holds true for kinetic averaging. For strong disorder,
i.e., the medium being close to the percolation point, we employ a field theory
for the nonlinear random resistor network in conjunction with a real-world
interpretation of Feynman diagrams, and we calculate the scaling exponents for
the shortest, the longest and the mean or average SAW to 2-loop order. In
addition, we calculate to 2-loop order the entire family of multifractal
exponents that governs the moments of the the statistical weights of the
elementary constituents (bonds or sites of the underlying fractal cluster)
contributing to the SAWs. Our RG analysis reveals that kinetic averaging leads
to renormalizability whereas static averaging does not, and hence, we argue
that the latter does not lead to a well-defined scaling limit. We discuss the
possible implications of this finding for experiments and numerical simulations
which have produced wide-spread results for the exponent of the average SAW. To
corroborate our results, we also study the well-known Meir-Harris model for
SAWs on percolation clusters. We demonstrate that this model leads back to
2-loop order to the renormalizable real world formulation with kinetic
averaging if the replica limit is consistently performed at the first possible
instant of the calculation.

28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol