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Related Experiment Videos

Escaping from cycles through a glass transition.

Sebastian Risau-Gusman1, Alexandre S Martinez, Osame Kinouchi

  • 1Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil. srisau@if.ufrgs.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 26, 2003
PubMed
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This study explores random walks in disordered media, revealing a glass transition in one dimension at a critical temperature. Below this temperature, walkers become trapped, exhibiting out-of-equilibrium behavior.

Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Random walks are fundamental models for diffusion in various media.
  • Disordered systems often exhibit complex behaviors like trapping and ergodicity breaking.

Purpose of the Study:

  • To investigate the behavior of a random walker in a d-dimensional disordered hypercube.
  • To identify conditions leading to glass transitions and out-of-equilibrium dynamics.

Main Methods:

  • Simulating a random walk with a distance-dependent transition probability (cost function E(D)).
  • Analyzing the system's behavior across different dimensions (d) and temperatures (T).
  • Investigating attractor basins and trapping times.

Main Results:

  • At T=0, the walk is deterministic, breaking ergodicity and leading to trapping in two-cycle attractors.

Related Experiment Videos

  • A glass transition occurs in d=1 at T(1)=1/2 (for N approaching infinity), where trapping time diverges.
  • Similar transitions are observed in higher dimensions with specific cost functions.

    • Conclusions:

    • The model exhibits a glass transition analogous to physical systems.
    • Out-of-equilibrium dynamics arise from walker trapping below the transition temperature.
    • The study provides insights into the statistical properties of spatial point processes.