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System size resonance in coupled noisy systems and in the Ising model

A. Pikovsky·A. Zaikin·M. A. de la Casa
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Abstract

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles -- lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.

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A. Pikovsky, A. Zaikin, M. A. de la Casa. 2001-12-18. System size resonance in coupled noisy systems and in the Ising model. https://doi.org/10.1103/physrevlett.88.050601

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