Abstract
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 temperatureT c and anomalous fluctuation belowT c 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.
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Saito, Y., Kubo, R. Nonlinearity in cooperative systems-dynamical Bethe-Ising model. J Stat Phys 15, 233–253 (1976). https://doi.org/10.1007/BF01012879
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DOI: https://doi.org/10.1007/BF01012879