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Universality classes for self-avoiding walks in a strongly disordered system.

Lidia A Braunstein1, Sergey V Buldyrev, Shlomo Havlin

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02115, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
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We investigated optimal self-avoiding walks (SAWs) in strong lattice disorder. Optimal SAWs in this extreme disorder are significantly more compact than previously studied paths.

Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Polymer physics

Background:

  • Self-avoiding walks (SAWs) are fundamental models in statistical physics.
  • Disordered systems present complex behaviors not seen in pure systems.
  • Strong disorder, characterized by a broad energy distribution, significantly alters path properties.

Purpose of the Study:

  • To investigate the behavior of self-avoiding walks (SAWs) in strong disorder on square and cubic lattices.
  • To determine the fractal dimension of optimal SAWs under extreme energy disorder.
  • To compare the compactness of these optimal SAWs with other related models.

Main Methods:

  • Simulated disorder using a probability distribution P(epsilon) proportional to 1/epsilon.
  • Studied the strong disorder limit for a broad range of energies.

Related Experiment Videos

  • Employed exact enumeration to find optimal SAWs of fixed length and origin.
  • Calculated fractal dimensions for optimal paths in 2D and 3D.

    • Main Results:

    • The fractal dimension of optimal SAWs in strong disorder was found to be d(opt)=1.52±0.10 in 2D and d(opt)=1.82±0.08 in 3D.
    • These optimal SAWs are significantly more compact than SAWs in uniform disorder or on percolation clusters.
    • Results suggest optimal SAWs in strong disorder may belong to the same universality class as maximal SAWs on percolation clusters.

    Conclusions:

    • Optimal self-avoiding walks in strong disorder exhibit distinct compact behavior.
    • The calculated fractal dimensions are consistent with universality class sharing with percolation models.
    • This study provides new insights into polymer behavior and pathfinding in complex, disordered environments.