Communications in Mathematical Physics

, Volume 51, Issue 3, pp 315–323 | Cite as

Percolation and phase transitions in the Ising model

  • Antonio Coniglio
  • Chiara Rosanna Nappi
  • Fulvio Peruggi
  • Lucio Russo
Article

Abstract

We give a description of the mechanism of phase transitions in the Ising model, pointing out the connection between the spontaneous magnetization and the existence of infinite clusters of “up” and “down” spins. The picture is more complete in the two-dimensional Ising model, where we can also use a generalized version of a result by Miyamoto.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Essam, J. W.: Percolation and cluster size. In: Phase Transitions and Critical Phenomena (C. Domb and M. S. Green, ed.), Vol. II. New York: Academic Press 1972Google Scholar
  2. 2.
    Coniglio, A.: Phys. Rev. B13, 2194–2207 (1976)Google Scholar
  3. 3.
    Miyamoto, M.: Commun. math. Phys.44, 169–173 (1975)Google Scholar
  4. 4.
    Harris, T. E.: Proc. Camb. Phil. Soc.43, 13–20 (1960)Google Scholar
  5. 5.
    Fortuin, C. M., Kasteleyn, P. W., Ginibre, J.: Commun. math. Phys.22, 89–103 (1971)Google Scholar
  6. 6.
    Lanford III, O. E., Ruelle, D.: Commun. math. Phys.13, 194–215 (1969)Google Scholar
  7. 7.
    Spitzer, F.: Am. Math. Monthly78, 142–154 (1971)Google Scholar
  8. 8.
    Holley, R.: Commun. math. Phys.36, 227–231 (1974)Google Scholar
  9. 9.
    Lebowitz, J., Martin-Löf, A.: Commun. math. Phys.25, 276–282 (1972)Google Scholar
  10. 10.
    Messager, A., Miracle-Sole, S.: Commun. math. Phys.40, 187–196 (1975)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Antonio Coniglio
    • 1
    • 2
  • Chiara Rosanna Nappi
    • 1
  • Fulvio Peruggi
    • 1
  • Lucio Russo
    • 1
    • 3
  1. 1.Istituto di Fisica TeoricaUniversità di NapoliNapoliItaly
  2. 2.C.N.R., Gruppo Nazionale di Struttura della MateriaItaly
  3. 3.C.N.R., Gruppo Nazionale di Fisica MatematicaItaly

Personalised recommendations