Skip to main content

On the validity of the replica method and its application to Ising chain in random field

  • III. Random Systems
  • Conference paper
  • First Online:
Static Critical Phenomena in Inhomogeneous Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 206))


Classical spin models in the presence of random interactions or external fields are considered. A general argument shows that the normal (non-Parisi-type) replica-trick is bound to yield the correct free energy provided that this latter is an analytic function of the strength ε of the random variables. As an illustration, the free energy of the one-dimensional Ising model in random external field is calculated up to sixth order in e by direct computation and also by the replica method, and the coincidence of the two results is demonstrated.

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

Access this chapter

Institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others


  1. S.F. Edwards and P.W. Anderson, J. Phys. F 5, 965 (1975)

    Article  ADS  Google Scholar 

  2. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975)

    Article  ADS  Google Scholar 

  3. J.L. van Hemmen and R.G. Palmer, J. Phys. A 12, 563 (1979)

    Article  ADS  Google Scholar 

  4. G. Györgyi and P. Ruján, J. Phys. C to appear

    Google Scholar 

  5. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979). J. Phys. A 13, L115; 1101; 1887 (1980)

    Article  ADS  Google Scholar 

  6. G. Toulouse, in Lecture Notes in Physics, Vol. 149 (Springer 1981)

    Google Scholar 

  7. R. Omari, J.J. Préjean and J. Souletie, J. Physique 44, 25 (1983)

    Google Scholar 

  8. G. Grinstein and D. Mukamel, Phys. Rev. B 27, 4503 (1983)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

A. Pękalski J. Sznajd

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Sütõ, A., Zimányi, G.T. (1984). On the validity of the replica method and its application to Ising chain in random field. In: Pękalski, A., Sznajd, J. (eds) Static Critical Phenomena in Inhomogeneous Systems. Lecture Notes in Physics, vol 206. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13369-8

  • Online ISBN: 978-3-540-38925-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics