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Effective ergodicity breaking phase transition in a driven-dissipative system
Sakib Matin1, Chon-Kit Pun1, Harvey Gould1,2
1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Physical Review. E
|March 15, 2020
Summary
The Olami-Feder-Christensen model shows a transition from ergodic to non-ergodic behavior as noise changes. This ergodicity breaking transition is characterized by changes in site stress and recurrence rates.
Area of Science:
- Complex systems
- Statistical physics
- Dynamical systems
Background:
- The Olami-Feder-Christensen (OFC) model is a sandpile model known for exhibiting self-organized criticality.
- Understanding the conditions under which such models transition between different dynamical regimes is crucial for complex systems research.
Purpose of the Study:
- To investigate the phenomenon of ergodicity breaking in the OFC model.
- To characterize the transition using concepts from dynamical systems and percolation theory.
Main Methods:
- Numerical simulations of the OFC model.
- Analysis of time-averaged stress on individual sites.
- Computation of recurrence plots and recurrence rates from dynamical system theory.
- Examination of clusters of failed sites using percolation theory.
Main Results:
- A clear transition to effective ergodicity breaking was observed as noise intensity was varied.
- Below a critical noise level, individual site stresses were trapped in limit cycles, indicating non-ergodicity.
- The average recurrence rate across all sites was identified as an order parameter, showing a distinct jump at the critical noise.
- Exponents characterizing the transition from above were found to be consistent with hyperscaling relations.
Conclusions:
- The OFC model exhibits an effective ergodicity breaking transition driven by noise intensity.
- Dynamical system measures like recurrence plots effectively characterize this transition.
- The transition shares characteristics with universality classes found in percolation theory.
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