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Slow relaxation, dynamic transitions, and extreme value statistics in disordered systems
K van Duijvendijk1, G Schehr, F van Wijland
1Laboratoire Matière et Systèmes Complexes, CNRS UMR 7057, Université de Paris VII, 10 rue Alice Domon et Léonie Duquet, Paris Cedex 13, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
Simple disordered models exhibit dynamics at a coexistence point between active and inactive phases. This dynamic phase transition is linked to extreme value statistics of the random energy landscape.
Area of Science:
- Statistical mechanics
- Complex systems dynamics
Background:
- Disordered systems, including the directed trap model and random energy model, are crucial for understanding complex phenomena.
- Characterizing the dynamical behavior of these models is essential for theoretical advancements.
Purpose of the Study:
- To investigate the dynamical behavior of simple disordered models.
- To identify the phase transitions governing their dynamics.
- To establish a connection between dynamics and the underlying energy landscape.
Main Methods:
- Analysis of the directed trap model and the random energy model.
- Identification of dynamical phases (active and inactive).
- Application of extreme value statistics to the random energy landscape.
Main Results:
- The dynamics of these models occur at a coexistence point of active and inactive phases.
- A dynamic phase transition is identified in these models.
- The phase transition is directly related to the extreme value statistics of the random energy landscape.
Conclusions:
- Simple disordered models exhibit a dynamic phase transition.
- Extreme value statistics of the energy landscape are key to understanding this transition.
- This finding provides a new perspective on the dynamics of disordered systems.
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