PMID- 12059668
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20020828
LR  - 20031103
IS  - 1539-3755 (Print)
IS  - 1539-3755 (Linking)
VI  - 65
IP  - 5 Pt 2
DP  - 2002 May
TI  - Universality classes for self-avoiding walks in a strongly disordered system.
PG  - 056128
AB  - We study the behavior of self-avoiding walks (SAWs) on square and cubic lattices 
      in the presence of strong disorder. We simulate the disorder by assigning random 
      energy epsilon taken from a probability distribution P(epsilon) to each site (or 
      bond) of the lattice. We study the strong disorder limit for an extremely broad 
      range of energies with P(epsilon) is proportional to 1/epsilon. For each 
      configuration of disorder, we find by exact enumeration the optimal SAW of fixed 
      length N and fixed origin that minimizes the sum of the energies of the visited 
      sites (or bonds). We find the fractal dimension of the optimal path to be 
      d(opt)=1.52+/-0.10 in two dimensions (2D) and d(opt)=1.82+/-0.08 in 3D. Our 
      results imply that SAWs in strong disorder with fixed N are much more compact 
      than SAWs in disordered media with a uniform distribution of energies, optimal 
      paths in strong disorder with fixed end-to-end distance R, and SAWs on a 
      percolation cluster. Our results are also consistent with the possibility that 
      SAWs in strong disorder belong to the same universality class as the maximal SAW 
      on a percolation cluster at criticality, for which we calculate the fractal 
      dimension d(max)=1.64+/-0.02 for 2D and d(max)=1.87+/-0.05 for 3D, values very 
      close to the fractal dimensions of the percolation backbone in 2D and 3D.
FAU - Braunstein, Lidia A
AU  - Braunstein LA
AD  - Center for Polymer Studies and Department of Physics, Boston University, Boston, 
      Massachusetts 02115, USA.
FAU - Buldyrev, Sergey V
AU  - Buldyrev SV
FAU - Havlin, Shlomo
AU  - Havlin S
FAU - Stanley, H Eugene
AU  - Stanley HE
LA  - eng
PT  - Journal Article
DEP - 20020521
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
EDAT- 2002/06/13 10:00
MHDA- 2002/06/13 10:01
CRDT- 2002/06/13 10:00
PHST- 2002/01/16 00:00 [received]
PHST- 2002/06/13 10:00 [pubmed]
PHST- 2002/06/13 10:01 [medline]
PHST- 2002/06/13 10:00 [entrez]
AID - 10.1103/PhysRevE.65.056128 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 2):056128. doi: 
      10.1103/PhysRevE.65.056128. Epub 2002 May 21.