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Related Experiment Videos

Directed self-avoiding walks in random media.

S B Santra1, W A Seitz, D J Klein

  • 1Texas A&M University at Galveston, Texas 77553-1675, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
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Self-avoiding walks (SAWs) on percolation clusters show slight swelling longitudinally. Transverse fluctuations exhibit a crossover from shrinking to swelling, with exponents remaining constant near the percolation threshold.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Self-avoiding walks (SAWs) are fundamental models in polymer physics and statistical mechanics.
  • Percolation theory studies the formation of clusters in random media.
  • Understanding walk behavior on disordered lattices is crucial for various physical phenomena.

Purpose of the Study:

  • To investigate the behavior of directed self-avoiding walks (SAWs) on infinite percolation clusters.
  • To analyze the longitudinal extension and transverse fluctuations of SAWs.
  • To determine the impact of random media on SAW properties near the percolation threshold.

Main Methods:

  • Monte Carlo simulations were employed to generate SAWs.
  • Two types of directed SAWs were studied: three-choice directed SAW and outwardly directed SAW.

Related Experiment Videos

  • Longitudinal extension R(N) and transverse fluctuation W(N) were measured as a function of the number of steps N.

    • Main Results:

    • A slight swelling was observed in the longitudinal direction on random lattices.
    • A crossover in transverse fluctuations from shrinking to swelling was identified at a specific walk length N(c).
    • Exponents governing transverse fluctuations remained unchanged even at the percolation threshold.

    Conclusions:

    • Directed SAWs exhibit distinct swelling behavior on percolation clusters compared to regular lattices.
    • The critical exponents for transverse fluctuations are robust to disorder near the percolation threshold.
    • The scaling function for SAW extensions on these random lattices was validated.