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Nonequilibrium dynamic transition in a kinetic Ising model driven by both deterministic modulation and correlated stochastic noises

Abstract

We report the nonequilibrium dynamical phase transition (NDPT) appearing in a kinetic Ising spin system (ISS) subject to the joint application of a deterministic external field and the stochastic mutually correlated noises simultaneously. A time-dependent Ginzburg-Landau stochastic differential equation, including an oscillating modulation and the correlated multiplicative and additive white noises, was addressed and the numerical solution to the relevant Fokker-Planck equation was presented on the basis of an average-period approach of driven field. The correlated white noises and the deterministic modulation induce a kind of dynamic symmetry-breaking order, analogous to the stochastic resonance in trend, in the kinetic ISS, and the reentrant transition has been observed between the dynamic disorder and order phases when the intensities of multiplicative and additive noises were changing. The dependencies of a dynamic order parameterQ upon the intensities of additive noiseA and multiplicative noiseM, the correlation λ between two noises, and the amplitude of applied external fieldh were investigated quantitatively and visualized vividly. Here a brief discussion is given to outline the underlying mechanism of the NDPT in a kinetic ISS driven by an external force and correlated noises.

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Correspondence to Yuanzhi Shao.

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Shao, Y., Zhong, W. & He, Z. Nonequilibrium dynamic transition in a kinetic Ising model driven by both deterministic modulation and correlated stochastic noises. Chin. Sci. Bull. 50, 2422–2426 (2005). https://doi.org/10.1007/BF03183630

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Keywords

  • Ising spin system
  • nonequilibrium dynamical phase transition
  • stochastic resonance
  • correlated noises
  • TDGL model