Self-Trapping Self-Repelling Random Walks

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• The true self-avoiding walk (SAW) model is a fundamental concept in statistical physics.
• Understanding walk dynamics on lattices is crucial for modeling various physical phenomena.

Purpose of the Study:

• To investigate a modified self-avoiding walk model with a spontaneous transition from self-repelling to self-trapping behavior.
• To analyze the properties of these walks, particularly their efficiency in covering finite lattices.

Main Methods:

• Modification of the true self-avoiding walk model.
• Analysis of walk dynamics on finite lattices.
• Characterization of the transition time T* and subdiffusive/intermittent regimes.

Main Results:

• Walks exhibit self-repelling behavior up to a characteristic time T*, then become self-trapping.
• On finite lattices, this transition is observable, leading to subdiffusive and intermittent walk dynamics.
• Despite intermittent behavior, these walks demonstrate high efficiency in covering finite lattices, as indicated by average cover times.

Conclusions:

• The modified self-avoiding walk model presents a unique dynamic, transitioning from repulsion to trapping.
• The observed subdiffusive and intermittent nature does not impede lattice covering efficiency.
• This model offers insights into complex system dynamics and lattice exploration strategies.