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## Stochastic resonance in
Ising model

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The phenomenon of stochastic resonance is an important recent discovery in
nonlinear science[1]. It concerns the counter-intuitive notion of optimal amplification
of signal in a stochastic setting when the noise level is finite. The Ising
model happens to have all the necessary ingredients of stochastic resonance
when considered as a set of coupled two-state oscillators in a stochastic, thermally
noisy environment[2]. Through a series of papers[3,4], this expectation have
now been fully confirmed.

Specifically, we studied stochastic resonance in the kinetic Ising model. The
input signal was taken to be a time-dependent magnetic field, and the noise
the temperature. We calculated several response functions for the magnetization[3]
and the signal-to-noise ratio[4], using linear-response theory, mean-field theory,
high-temperature expansion, phenomenological arguments, time-dependent Ginzburg-Landau
equation and computer simulations. A novel resonance temperature T_r above T_c
was identified in the signal-to-noise ratio, with its origin elucidated and
related to critical slowing down. Through mappings between the Ising model and
physical systems (magnetic ones, binary alloys and fluids), we hope to stimulate
new experimental exploration of stochastic resonance.

### References

- For a comprehensive review, see, e.g., L. Gammaitoni, P.
Hanggi, P. Jung and F. Marchesoni, Rev. Mod. Phys.
**70**, 223 (1998)
- Z. Neda, Phys. Rev. E
**51**, 5315 (1995); Z. Neda, Phys.
Lett. A **210**, 125 (1996).
**Response in kinetic Ising model to oscillating magnetic
fields,**

K.-t. Leung and Z. Neda, Phys. Lett. A **246**,
505 (1998).

Also e-print cond-mat/9804251.
**Non-trivial stochastic resonance temperature for the kinetic
Ising models,**

K.-t. Leung and Z. Neda, Phys. Rev. E **59**,
2730 (1999).

Last revised
October 7, 2002
©KtL