Skip to main content
Log in

Transition probabilities and stochastic equations for the mean field ising model

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The microscopic transition rate is briefly calculated from quantum principles to derive the microscopic master equation. By introducing τp, the phenomenological time, and coarse graining Wp, the transition rate, a complete normalized phenomenological transition rate is obtained. The Langer form is then approximately obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. S. Langer,Ann. Phys. (N.Y.) 54:258 (1969).

    Google Scholar 

  2. J. S. Langer,Ann. Phys. (N.Y.) 65:53 (1971).

    Google Scholar 

  3. H. Metiu, K. Kitahara, and J. Ross,J. Chem. Phys. 63:5116 (1975).

    Google Scholar 

  4. L. Van Hove, inLectures on Statistical Mechanics of Nonequilibrtum Phenomena, C. de Witt and J. F. Detoeuf, eds., John Wiley, New York (1960).

    Google Scholar 

  5. L. Landau and E. Teller,Phys. Z. Sowjetunion 10:34 (1936); F. Bloch,Phys. Rev. 105:1206 (1957); P. N. Argyres and P. L. Kelley,Phys. Rev. 134:A98 (1964); E. B. Davies,Quantum Theory of Open Systems, Academic, New York (1976); W. Peier,Physica 57:565 (1972).

    Google Scholar 

  6. R. Griffiths, C. Y. Weng, and J. Langer,Phys. Rev. 149:301 (1966).

    Google Scholar 

  7. G. Arfken,Mathematical Methods for Physicists, Academic, New York (1970).

    Google Scholar 

  8. E. Montroll, inEnergetics in Metallurgical Phenomena, Vol. III, W. Mueller, ed., Gordon and Breach, New York (1967).

    Google Scholar 

  9. M. N. Barber and B. W. Ninham,Random and Restricted Walks, Gordon and Breach, New York (1970).

    Google Scholar 

  10. D. Bedeaux, K. L. Lindenberg, and K. E. Shuler,J. Math. Phys. (N.Y.) 12:2116 (1971).

    Google Scholar 

  11. R. Balescu,Equilibrium and Nonequilibrium Statistical Mechanics, John Wiley & Sons, New York (1975).

    Google Scholar 

  12. L. Arnold, W. Horsthemke, and R. Lefever,Z. Phys. B29:367 (1978); W. Horsthemke and R. Lefever,Phys. Lett. 64A:19 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by the Robert A. Welch Foundation.

On leave of absence from the Institute of Theoretical Physics, Academia Sinica, Beijing, China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng, W.M., Schieve, W.C. Transition probabilities and stochastic equations for the mean field ising model. J Stat Phys 29, 375–385 (1982). https://doi.org/10.1007/BF01020793

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01020793

Key words

Navigation