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First-order like phase transition induced by quenched coupling disorder
Hyunsuk Hong1, Erik A Martens2
1Department of Physics and Research Institute of Physics and Chemistry, Jeonbuk National University, Jeonju 54896, South Korea.
Chaos (Woodbury, N.Y.)
|July 1, 2022
Summary
We studied coupled oscillators with random interactions and thermal noise. The system shows a universal synchronization threshold, unaffected by noise or coupling randomness.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- Understanding collective dynamics and synchronization in coupled oscillator systems is crucial for various scientific fields.
- The influence of non-separable, random interactions and thermal noise on synchronization transitions remains an active area of research.
Purpose of the Study:
- To investigate the collective dynamics of XY model-type oscillators with non-separable random interactions under thermal noise.
- To derive and validate theoretical formulas for critical synchronization thresholds in both deterministic and stochastic regimes.
- To explore the universality of synchronization phenomena in heterogeneous network structures.
Main Methods:
- Analysis of collective dynamics using stability analysis for finite populations and mean-field theory with graphons for the thermodynamic limit.
- Derivation of exact formulas for critical transition thresholds in deterministic (T=0) and stochastic (T>0) cases.
- Extensive numerical simulations to support theoretical findings.
Main Results:
- At T=0, a discontinuous, first-order-like phase transition from incoherence to full coherence is observed.
- For T>0, the transition from incoherence to partial coherence becomes continuous, with a higher critical threshold.
- The derived synchronization threshold is identical to that found in systems with uniform node strengths, suggesting universality.
Conclusions:
- The study provides a rigorous theoretical framework for understanding synchronization in complex oscillator networks with random interactions.
- Thermal noise alters the nature of the phase transition, making it continuous and increasing the synchronization threshold.
- The observed universality of the synchronization threshold highlights fundamental principles governing collective behavior in diverse network topologies.
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