Skip to main content
SpringerLink
Log in

The Ising Model and the Diophantine Moment Problem

  • Conference paper
Book cover Number Theory and Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 47))

  • 426 Accesses

Abstract

The thermodynamical quantities which occur in the Ising model can be derived from the generating function of the moments of a measure with support on a finite interval. The moments belong either to a ring of polynomials with integer coefficients or to the ring of natural integers. Some general results are given on the nature of the possible generating functions once some additional assumptions are made about the support of the measure.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin Inc., Reading, Mass., 1969.

    MATH  Google Scholar 

  2. C. Domb, Advances in Physics, 9, p. 149–361, 1960.

    Article  ADS  Google Scholar 

  3. R. B. Griffiths, Rigorous results and theorems, in “Phase Transitions and Critical Phenomena”, C. Domb and M. S. Green eds., Academic Press, vol. 1, p. 7–104, 1972.

    Google Scholar 

  4. C. Domb, Ising models, in “Phase Transitions and Critical Phenomena”, C. Domb and M. S. Green eds., Academic Press, vol. 3, p. 357–484, 1974.

    Google Scholar 

  5. C. N. Yang and T. D. Lee, Phys. Rev. 87, 404–409, 1952

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. T. D. Lee and C. N. Yang 87, 410–419, 1952

    Google Scholar 

  7. D. Ruelle, Phys. Rev. Lett. 26, 303–304, 1971

    Article  MathSciNet  ADS  Google Scholar 

  8. D. Ruelle, Commun. Math. Phys. 31, 265–277, 1973

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. J. D. Bessis, J. M. Drouffe and P. Moussa, J. Phys. A.: Math. Gen. 9, 2105–2124, 1976

    Article  ADS  Google Scholar 

  10. M. Barnsley, D. Bessis and P. Moussa, J. Math. Phys. 20, 535–546, 1979

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. P. Moussa, Ann. Inst. Henri Poincaré, 28 A, 309–347, 1983

    Google Scholar 

  12. V. S. Vladimirov and I. V. Volovitch, Teoreticheskaya i Mathematicheskaya Fizika, 53, 3–15, 1982, English translation: Theor. Math. Phys., 53, 943–951, 1982

    ADS  Google Scholar 

  13. H. Helson, Proc. Am. Math. Soc. 4, 686–691, 1953, and: T.Itô and I. Amemiya, Bull. Amer. Math. Soc. 70, 774–778, 1964

    Article  Google Scholar 

  14. H. Brolin, Arkiv For Mat. 6, 103–144, 1965

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. R. C. Buck, Duke Math. J. 15, 879–891, 1948

    Article  MathSciNet  MATH  Google Scholar 

  16. E. Hewitt and H. S. Zuckerman, Duke Math.J. 26, 305–324, 1959

    Article  MathSciNet  MATH  Google Scholar 

  17. D. H. Lehmer, Ann. Math. 34, 461–479, 1933 M. Waldschmidt, L’Enseignement Mathématique, 26 Série II, 201–209,

    Article  MathSciNet  MATH  Google Scholar 

  18. P. Moussa, J. S. Geronimo, D. Bessis, C. R. Acad. Se. Paris 299, Série I, 281–284, 1984

    Google Scholar 

  19. L. Onsager, Phys. Rev. 65, 117–149, 1944

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. C. N. Yang, Phys. Rev. 85, 808–816, 1952

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Service de Physique Théorique, CEN Saclay, F-91191, Gif-sur-Yvette Cedex, France

    P. Moussa

Authors
  1. P. Moussa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Service de Physique Théorique, C.E.N Saclay, F-91191, Gif-sur-Yvette Cedex, France

    Jean-Marc Luck  & Pierre Moussa  & 

  2. Institut Henri-Poincaré, Problèmes Diophantiens, Université de Paris 6, F-75231, Paris Cedex 05, France

    Michel Waldschmidt

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Moussa, P. (1990). The Ising Model and the Diophantine Moment Problem. In: Luck, JM., Moussa, P., Waldschmidt, M. (eds) Number Theory and Physics. Springer Proceedings in Physics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75405-0_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-75405-0_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-75407-4

  • Online ISBN: 978-3-642-75405-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation