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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

Summary

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.

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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.
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.

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