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Noise effects in a finite-size Ising-like model
Iurii Gudyma1, Artur Maksymov, Seiji Miyashita
1Department of General Physics, Chernivtsi National University, 58012 Chernivtsi, Ukraine.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
Summary
Finite systems with long-range interactions exhibit distinct ordered states. Noise and system size influence stationary properties and dynamics, affecting transition times.
Area of Science:
- Statistical Physics
- Complex Systems
- Nonlinear Dynamics
Background:
- Bistable systems with long-range interactions are crucial models in various scientific fields.
- Understanding finite-size effects is essential for accurately describing real-world systems.
- The influence of noise on system dynamics is a key area of research.
Purpose of the Study:
- To investigate finite-size effects on the stationary state and transient dynamics of a bistable system.
- To analyze the impact of different noise types on system behavior.
- To explore the characteristics of the probability distribution in finite systems.
Main Methods:
- Utilized an Ising-like model with infinite range interaction (Husimi-Temperlay model).
- Formulated the problem using the Langevin equation to incorporate various noise types.
- Analyzed the probability of the stationary state and mean first-passage times.
Main Results:
- Identified two distinct regions within the ordered state: saturated and transient.
- The saturated region shows distribution maxima at the extreme Ising variable values (±1).
- The transient region exhibits distribution maxima at non-saturated values, influenced by finite size and noise.
Conclusions:
- Finite-size effects significantly alter the stationary state properties and dynamics of bistable systems.
- The introduction of thermal bath coupling noise provides further insights into system fluctuations.
- Mean first-passage times reveal finite-size impacts on the system's dynamical behavior.
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