Chinese Science Bulletin

, Volume 50, Issue 21, pp 2422–2426 | Cite as

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

  • Yuanzhi Shao
  • Weirong Zhong
  • Zhenhui He


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.


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Landau, D. P., Binder, K., A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge: Cambridge University Press, 2000, 15, 78.Google Scholar
  2. 2.
    Chakrabrati, B. K., Acharyya, M., Dynamic transitions and hysteresis, Rev. Mod. Phys., 1999, 71: 847–859.CrossRefGoogle Scholar
  3. 3.
    Sides, S. W., Rikvold, P. A., Novotny, M. A., Kinetic Ising model in an oscillating field: Finite-size scaling at the dynamic phase transition, Phys. Rev. Lett., 1998, 81: 834–837.CrossRefGoogle Scholar
  4. 4.
    Acharyya, M., Nonequilibrium phase transition in the kinetic Ising model: Existence of a tricritical point and stochastic resonance, Phys. Rev. E, 1999, 59: 218–221.CrossRefGoogle Scholar
  5. 5.
    Acharyya, M., Chakrabrati, B. K., Response of Ising systems to oscillating and pulsed fields: Hysteresis, ac, and pulse susceptibility, Phys. Rev. B, 1995, 52: 6550–6568.CrossRefGoogle Scholar
  6. 6.
    Korniss, G., Rikvold, P. A., Novotny, M. A., Absence of first-order transition and tricritical point in the dynamic phase diagram of a spatially extended bistable system in an oscillating field, Phys. Rev. E, 2002, 66: 056127–1-12.CrossRefGoogle Scholar
  7. 7.
    Shao, Y. Z., Lai, J. K. L., Shek, C. H., Lin, G. M., Lan, T., Nonequilibrium dynamical phase transition of 3D kinetic Ising/ Heisenberg spin system, Chinese Physics, 2004, 13: 0243–0250.CrossRefGoogle Scholar
  8. 8.
    Fujisaka, H., Tutu, H., Rikvold, P. A., Dynamic phase transition in a time-dependent Ginzburg-Landau model in an oscillating field, Phys. Rev. E, 2001, 63: 036109–1-11.CrossRefGoogle Scholar
  9. 9.
    Gammaitoni, L., Hanggi, P., Jung, P., Marchesoni, F., Stochastic resonance, Rev. Mod. Phys., 1998, 70: 223–287.CrossRefGoogle Scholar
  10. 10.
    Anishchenko, V. S., Astakhov, V. V., Neiman, A. B., Vadivasova, T. E., Schimansky-Geier, L., Nonlinear Dynamics of Chaotic and Stochastic Systems, Berlin/Heidelberg: Springer-Verlag, 2002, 327–363.Google Scholar
  11. 11.
    Qi Anshen, Du Chanying, Nonliear Model of Immunity (in Chinese), Shanghai: Shanghai Scientific and Technological Education Publishing House, 1998, 124–149.Google Scholar
  12. 12.
    Hu, G., Stochastic Forces and Nonlinear Systems (in Chinese), Shanghai: Shanghai Scientific and Technological Education Publishing House, 1994.Google Scholar
  13. 13.
    Zaikin, A. A., Kurths, J., Schimansky-Geier, L., Doubly stochastic resonance, Phys. Rev. Lett., 2000, 85: 227–231.CrossRefGoogle Scholar
  14. 14.
    Jia, Y., Yu, S. N., Li, J. R., Stochastic resonance in a bistable system subject to multiplicative and additive noises, Phys. Rev. E, 2000, 62: 1869–1878.CrossRefGoogle Scholar
  15. 15.
    Jia, Y., Li, J. R., Reentrance phenomena in a bistable kinetic model driven by correlated noise, Phys. Rev. Lett., 1997, 78: 994–997.CrossRefGoogle Scholar
  16. 16.
    Denisov, S. I., Vitrenko, A. N., Horsthemke, W., Nonequilibrium transitions induced by the cross-correlation of white noises, Phys. Rev. E, 2003, 68: 046132–1-5.CrossRefGoogle Scholar
  17. 17.
    Russell, D. F., Wilkens, L. A., Moss, F., Use of behavioural stochastic resonance by paddle fish for feeding, Nature, 1999, 402: 291–294.CrossRefGoogle Scholar
  18. 18.
    Shao Yuanzhi, Zhong Weirong, Lin Guangming, Nonequilibrium dynamic phase transition of an Ising spin system driven by various oscillationg field, Acta Physica Sinica (in Chinese), 2004, 53: 3165–3170.Google Scholar
  19. 19.
    Shao Yuanzhi, Zhong Weirong, Lin Guangming, Li Jianchan, Stochastic resonance of an Ising spin system driven by stochasti exteranl field, Acta Physica Sinica (in Chinese), 2004, 53: 3157–3164.Google Scholar
  20. 20.
    Chatterjee, A., Chakrabrati, B. K., Competing field pluse induced dynamic transition in Ising models. arXiv:cond-mat/0312454 v2 21 Jan 2004.Google Scholar
  21. 21.
    Zhong Weirong, Shao Yuanzhi, He Zhenhui, Stochastic resonance in the growth of a tumor induced by correlated noises, Chinese Science Bulletin, 2005, 50(20): 2273–2275.CrossRefGoogle Scholar
  22. 22.
    Bloembergen, N., Wang, S., Relaxation effects in para- and ferromagnetic resonance, Phys. Rev., 1954, 93: 72–83.CrossRefGoogle Scholar
  23. 23.
    Kim, B. J., Minnhagen, P., Kim, H. J., Choi, M. Y., Jeon, G. S., Double stochastic resonance peak in systems with dynamic phase transitions, Europhys. Lett. 2001, 56: 333–339.CrossRefGoogle Scholar

Copyright information

© Science in China Press 2005

Authors and Affiliations

  1. 1.Department of PhysicsSun Yat-Sen UniversityGuangzhouChina

Personalised recommendations