Stochastic resonance in Ising model


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.


  1. For a comprehensive review, see, e.g., L. Gammaitoni, P. Hanggi, P. Jung and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)
  2. Z. Neda, Phys. Rev. E 51, 5315 (1995); Z. Neda, Phys. Lett. A 210, 125 (1996).
  3. 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.
  4. 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