Problème diophantien des moments et modèle d'Ising

Pierre Moussa

Recherche Coopérative sur Programme n°25 (1982)

  • Volume: 30, page 1-41

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Moussa, Pierre. "Problème diophantien des moments et modèle d'Ising." Recherche Coopérative sur Programme n°25 30 (1982): 1-41. <http://eudml.org/doc/274613>.

@article{Moussa1982,
author = {Moussa, Pierre},
journal = {Recherche Coopérative sur Programme n°25},
keywords = {generating function; polynomial ring; diophantine moment problem; positive measure; discrete measure; thermodynamical parameters of the Ising model},
language = {fre},
pages = {1-41},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Problème diophantien des moments et modèle d'Ising},
url = {http://eudml.org/doc/274613},
volume = {30},
year = {1982},
}

TY - JOUR
AU - Moussa, Pierre
TI - Problème diophantien des moments et modèle d'Ising
JO - Recherche Coopérative sur Programme n°25
PY - 1982
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 30
SP - 1
EP - 41
LA - fre
KW - generating function; polynomial ring; diophantine moment problem; positive measure; discrete measure; thermodynamical parameters of the Ising model
UR - http://eudml.org/doc/274613
ER -

References

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  1. [1] M. Barnsley, D. Bessis, and P. Moussa, J. Math. Phys. Vol 20, p 535, 1979 Zbl0454.44006MR529718
  2. [2] Pour plus détails sur le modèle d'Ising, voir par exemple l'article de revue "On the theory of cooperative phenomena in crystals" de C. Domb, Advances in Physics, Vol IX, p 149, 1960 
  3. [3] T.D. Lee and C.N. Yang, Phys. Rev. Vol 87, p 410, 1952 Zbl0048.43401
  4. [4] D. Ruelle, Phys. Rev. Lett. Vol 26, p 303, 1971 MR292441
  5. D. RuelleCommun. Math. Phys. Vol 31, p 265, 1973 Zbl1125.82311MR353912
  6. [5] C.N. Yang and T.D. Lee, Phys. Rev. Vol 87, p 404, 1952 Zbl0048.43305
  7. [6] C. Domb, in "Phase transition and critical phenomena", C. Domb and M.S. Green, editors, Vol 3, p 357, Academic Press, New-York, 1974 Zbl1063.82001MR353911
  8. [7] J.D. Bessis, J.M. Drouffe, and P. Moussa, J. Phys. A : Math. Gen. Vol 9, p 2105, 1976 
  9. [8] E. Hewitt and H.S. Zuckerman, Duke Mathematical Journal, Vol 26, p 305, 1959 Zbl0087.05802MR149164
  10. [9] D. Bessis, in "Bifurcation phenomena in mathematical physics and related topics", C. Bardos and D. Bessis editors, Nato Advanced Study Institute Series, Series C, Vol 54, p 203, D. Reidel Publishing Company1980 Zbl0425.00010MR580287
  11. [10] P. Dienes, "The Taylor series", Dover, New-York, 1957, p 324 Zbl0078.05901MR89895JFM57.0339.10
  12. [11] Voir l'article de revue "Uber potenzreihen, die irrationale funktionen darstellen" I, "Uberblicke Mathematik", Vol 6, p 179, 1973 et MR372166
  13. "Uber potenzreihen, die irrationale funktionen darstellen" II, "Uberblicke Mathematik", Vol 7, p 7, 1974. Zbl0311.30002MR372167
  14. Les références originales sont : G. Polya, Proceedings of the London Mathematical Society (2), Vol 21, p 22, 1923 et 
  15. F. Carlson, Mathematische Zeitschrift, Vol 9, p 1, 1921 JFM48.1208.02
  16. [12] U. Grenander and G. Szegö, "Toeplitz forms and their applications" University of California Press, 1958 Zbl0080.09501MR94840
  17. [13] Voir par exemple A. Zygmund, "Trygonometric series", Cambridge University Press, 1968, Vol II, p 150 Zbl0085.05601
  18. [14] F. Gramain, "Fonctions entières arithmétiques", séminaire Delange-Pisot-Poitou, 19è année, 1977/1978, n°8, Paris) Zbl0402.10034MR520304
  19. [15] R. Creighton Buck, Duke Mathematical journal, Vol 15 page 879, 1948 Zbl0033.36402MR29984
  20. [16] D. Bessis, M.L. Mehta and P. Moussa, "Orthogonal polynomials on a family of Cantor sets and the problem of iteration of quadratic mappings" Preprint Saclay DPh-T/81/79, à paraître en 1982 "Letters in Mathematical Physics" Zbl0483.33006MR651127

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