Skip to main content
Log in

The Curie–Weiss model with Complex Temperature: Phase Transitions

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

Abstract

We study the partition function of the Curie–Weiss model with complex temperature, and partially describe its phase transitions. As a consequence, we obtain information on the locations of zeros of the partition function (the Fisher zeros).

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.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Anderson, G.W., Guionnet, A., Zeitouni, O.: An introduction to Random Matrices. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  2. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, 2nd edn. Springer, New York (1998)

    Book  MATH  Google Scholar 

  3. Ellis, R.S., Newman, C.M.: Limit theorems for sums of dependent random variables occuring in statistical mechanics. Probab. Theory Relat. Fields 44, 117–139 (1978)

    MATH  Google Scholar 

  4. Fisher, M.E.: The Nature of Critical Points. Lecture Notes in Theoretical Physics, vol. 7c, pp. 1–159. University of Colorado Press, Boulder (1965)

    Google Scholar 

  5. Glasser, M.L., Privman, V., Schulman, L.S.: Complex temperature plane zeros in the mean-field approximation. J. Stat. Physics 45, 451–457 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  6. Krasnytska, M., Berche, B., Holovatch, Yu., Kenna, R.: Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks. J. Phys. A 49(13), 135001 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Kitanine, N., Maillet, J.M., Slavnov, N.A., Terras, V.: Large distance asymptotic behavior of the emptiness formation probability of the \(XXZ\) spin-\(\frac{1}{2}\) Heisenberg chain. J. Phys. A 35, L735–10502 (2002)

    MATH  Google Scholar 

  8. Levinson, N.: Transformation of an analytic function of several variables to a canonical form. Duke Math. J. 28, 345–353 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  9. Martin, J.: Integrals with a large parameter and several nearly coincident saddle points; the continuation of uniformly asymptotic expansions. Math. Proc. Camb. Philos. Soc. 76(1), 211–231 (1974)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Martin-Löf, A.: A Laplace approximation for sums of independent random variables. Z. Wahr. ver. Geb. 59, 101–115 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yang, C.N., Lee, T.D.: Statistical theory of equations of state and phase transitions, I. Theory of condensation. Phys. Rev. 87(3), 404–409 (1952)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Supported in part by ISF Grant 147/15.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mira Shamis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shamis, M., Zeitouni, O. The Curie–Weiss model with Complex Temperature: Phase Transitions. J Stat Phys 172, 569–591 (2018). https://doi.org/10.1007/s10955-017-1812-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-017-1812-0

Keywords

Navigation