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Discontinuous transitions in globally coupled potential systems with additive noise
Rüdiger Kürsten1,2,3, Ulrich Behn1,2
1Institut für Theoretische Physik, Universität Leipzig, POB 100 920, D-04009 Leipzig, Germany.
Physical Review. E
|January 14, 2017
Summary
This study investigates phase transitions in globally coupled systems with noise. Adding nonlinearity creates new phases and transitions, with finite system simulations revealing distinct behaviors from infinite systems.
Area of Science:
- Statistical physics
- Nonlinear dynamics
- Complex systems
Background:
- Investigates globally coupled overdamped constituents in a double-well potential with nth order saturation and Gaussian white noise.
- Examines phase transitions from symmetric to symmetry-broken phases, finding qualitative behavior independent of the saturation order 'n'.
Purpose of the Study:
- To analyze phase transitions in a globally coupled system with a double-well potential and noise.
- To explore the effects of introducing additional nonlinearity, leading to a potential with up to three minima.
- To investigate the behavior of finite systems in the coexistence region.
Main Methods:
- Analytical calculation of critical points for strong and weak noise limits.
- Characterization of phase transitions (continuous and discontinuous).
- Numerical simulations of finite systems in the coexistence region.
Main Results:
- Continuous phase transition from symmetric to symmetry-broken phase, independent of 'n'.
- Introduction of additional nonlinearity creates three parameter space regions: symmetric, broken symmetry, and coexistence.
- Discontinuous transition at the boundary of the coexistence region; continuous transition otherwise.
- Calculated strong and weak noise limits for the tricritical point, forming tight bounds.
- Simulations show finite systems differ from infinite systems in the coexistence region, indicating non-commuting limits.
Conclusions:
- The system exhibits continuous phase transitions, with behavior robust to saturation order.
- Additional nonlinearity enriches the system's dynamics, leading to distinct phase regions and transition types.
- Finite system size and stationarity limits do not commute, highlighting crucial differences in finite versus infinite systems.
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