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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.