PMID- 22400528
OWN - NLM
STAT- MEDLINE
DCOM- 20120514
LR  - 20120309
IS  - 1550-2376 (Electronic)
IS  - 1539-3755 (Linking)
VI  - 85
IP  - 1 Pt 1
DP  - 2012 Jan
TI  - Linear polymers in disordered media: the shortest, the longest, and the mean 
      self-avoiding walk on percolation clusters.
PG  - 011123
AB  - Long linear polymers in strongly disordered media are well described by 
      self-avoiding walks (SAWs) on percolation clusters and a lot can be learned about 
      the statistics of these polymers by studying the length distribution of SAWs on 
      percolation clusters. This distribution encompasses 2 distinct averages, viz., 
      the average over the conformations of the underlying cluster and the 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, this disorder is redundant in the 
      sense the renormalization group; i.e., differences to the ordered case appear 
      merely in nonuniversal quantities. Using dynamical field theory, we show that the 
      same holds true for kinetic averaging. Our main focus, however, lies on strong 
      disorder, i.e., the medium being close to the percolation point, where disorder 
      is relevant. Employing a field theory for the nonlinear random resistor network 
      in conjunction with a real-world interpretation of the corresponding Feynman 
      diagrams, 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 widespread 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 the 
      Meir-Harris model leads back up 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 in the course of the calculation.
CI  - (c) 2012 American Physical Society
FAU - Janssen, Hans-Karl
AU  - Janssen HK
AD  - Institut fur Theoretische Physik III, Heinrich-Heine-Universitat, D-40225 
      Dusseldorf, Germany.
FAU - Stenull, Olaf
AU  - Stenull O
LA  - eng
PT  - Journal Article
PT  - Research Support, U.S. Gov't, Non-P.H.S.
DEP - 20120113
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
RN  - 0 (Polymers)
SB  - IM
MH  - Computer Simulation
MH  - Diffusion
MH  - *Models, Chemical
MH  - *Models, Molecular
MH  - Polymers/*chemistry
EDAT- 2012/03/10 06:00
MHDA- 2012/05/15 06:00
CRDT- 2012/03/10 06:00
PHST- 2011/11/22 00:00 [received]
PHST- 2012/03/10 06:00 [entrez]
PHST- 2012/03/10 06:00 [pubmed]
PHST- 2012/05/15 06:00 [medline]
AID - 10.1103/PhysRevE.85.011123 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):011123. doi: 
      10.1103/PhysRevE.85.011123. Epub 2012 Jan 13.