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Phase diagram of optimal paths.

Alex Hansen1, János Kertész

  • 1Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Alex.Hansen@phys.ntnu.no

Physical Review Letters
|August 25, 2004
PubMed
Summary

This study links optimal path searches in disordered media to diverse problems like percolation and polymers. A new algorithm and simulations reveal a strong-disorder phase with self-affine paths.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Computational Physics

Background:

  • Disordered media present complex challenges in understanding emergent phenomena.
  • Optimal path searches are fundamental in various physical systems.

Purpose of the Study:

  • To unify diverse problems in disordered media under a common framework of optimal path searches.
  • To introduce an efficient algorithm for solving d-dimensional models.
  • To investigate the phase diagram of the directed polymer universality class.

Main Methods:

  • Developing a generalized framework for optimal path searches by tuning randomness distributions.
  • Implementing a novel, efficient numerical algorithm with complexity O(N(1+df/d)).
  • Conducting extensive two-dimensional simulations to map phase boundaries.

Main Results:

  • Established a unified approach linking directed percolation, invasion percolation, and spanning polymers.
  • Identified a novel strong-disorder phase characterized by self-affine optimal paths.
  • Determined parameter-dependent scaling exponents for the strong-disorder phase.

Conclusions:

  • The proposed framework effectively connects various disordered systems.
  • The identified strong-disorder phase represents a new universality class.
  • The efficient algorithm facilitates further numerical exploration of these complex systems.

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