Journal of Statistical Physics

, Volume 15, Issue 3, pp 233–253

Nonlinearity in cooperative systems-dynamical Bethe-Ising model

  • Yukio Saito
  • Ryogo Kubo

DOI: 10.1007/BF01012879

Cite this article as:
Saito, Y. & Kubo, R. J Stat Phys (1976) 15: 233. doi:10.1007/BF01012879


The dynamics of the short-range order as well as the long-range order in the nonlinear cooperative system is investigated specifically for a kinetic Ising model in the Bethe approximation. The phenomena of critical slowing down near the transition temperatureTc and anomalous fluctuation belowTc are directly related to the instability of the long-range order. The dynamics of the short-range order is essentially a fast mode and is noncritical. However, through the nonlinear coupling the short-range order is also influenced by the critical behavior of the long-range order.

Key words

Kinetic Ising model quasi-chemical approximation critical slowing down anomalous fluctuations far from equilibrium coupling between order parameters 

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Yukio Saito
    • 1
  • Ryogo Kubo
    • 1
  1. 1.Department of PhysicsUniversity of TokyoTokyoJapan

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