Problème diophantien des moments et modèle d'Ising

Pierre Moussa

Annales de l'I.H.P. Physique théorique (1983)

  • Volume: 38, Issue: 4, page 309-348
  • ISSN: 0246-0211

How to cite

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Moussa, Pierre. "Problème diophantien des moments et modèle d'Ising." Annales de l'I.H.P. Physique théorique 38.4 (1983): 309-348. <http://eudml.org/doc/76201>.

@article{Moussa1983,
author = {Moussa, Pierre},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {generating function; polynomial ring; diophantine moment problem; positive measure; discrete measure; thermodynamical parameters of the Ising model},
language = {fre},
number = {4},
pages = {309-348},
publisher = {Gauthier-Villars},
title = {Problème diophantien des moments et modèle d'Ising},
url = {http://eudml.org/doc/76201},
volume = {38},
year = {1983},
}

TY - JOUR
AU - Moussa, Pierre
TI - Problème diophantien des moments et modèle d'Ising
JO - Annales de l'I.H.P. Physique théorique
PY - 1983
PB - Gauthier-Villars
VL - 38
IS - 4
SP - 309
EP - 348
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/76201
ER -

References

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  1. [1] M. Barnsley, D. Bessis, and P. Moussa, J. Math. Phys., t. 20, 1979, p. 535. Zbl0454.44006MR529718
  2. [2] Pour plus de 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, t. IX, 1960, p. 149. 
  3. [3] T.D. Lee and C.N. Yang, Phys. Rev., t. 87, 1952, p. 410. Zbl0048.43401
  4. [4] D. Ruelle, Phys. Rev. Lett., t. 26, 1971, p. 303 et Commun. Math. Phys., t. 31, 1973, p. 265. MR292441
  5. [5] C.N. Yang and T.D. Lee, Phys. Rev., t. 87, 1952, p. 404. Zbl0048.43305
  6. [6] C. Domb, in Phase transition and critical phenomena, C. Domb and M. S. Green, editors, Academic Press, New York, t. 3, 1974, p. 357. MR353911
  7. [7] J.D. Bessis, J.M. Drouffe and P. Moussa, J. Phys. A : Math. Gen., t. 9, 1976, p. 2105. 
  8. [8] E. Hewitt and H.S. Zuckerman, Duke Mathematical Journal, t. 26, 1959, p. 305. Zbl0087.05802MR149164
  9. [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, t. 54, p. 203, D. Reidel, Publishing Company, 1980. MR580287
  10. [10] P. Dienes, The Taylor series, Dover, New York, 1957, p. 324. Zbl0078.05901MR89895
  11. [11] Voir l'article de revue : Über potenzreihem, die irrationale funktionen darstellen (I et II). Uberblicke Mathematik, t. 6, 1973, p. 179 et t. 7, 1974, p. 7. Les réfé- rences originales sont : G. Polya, Proceedings of the London Mathematical Society (2), t. 21, 1923, p. 22 et F. Carlson, Mathematische Zeitschrift, t. 9, 1921, p. 1. 
  12. [12] U. Grenander and G. Szegö, Toeplitz forms and their applications, University of California Press, 1958. Zbl0080.09501MR94840
  13. [13] Voir par exemple A. Zygmund, Trigonometric series, Cambridge University Press, t. II, 1968, p. 150. 
  14. [14] F. Gramain, Fonctions entières arithmétiques, séminaire Delange-Pisot-Poitou, 19e année, 1977/1978, n° 8, Paris. Zbl0402.10034MR520304
  15. [15] R. Creighton Buck, Duke Mathematical journal, t. 15, 1948, p. 879. Zbl0033.36402MR29984
  16. [16] D. Bessis, M.L. Mehta and P. Moussa, Letters in Mathematical Physics, t. 6, 1982, p. 123. Zbl0483.33006MR651127
  17. [17] D. Bessis, M.L. Mehta et P. Moussa, C. R. Acad. Sci. Paris, t. 293, Série 1, 1981, p. 705. Zbl0493.33014MR650541
  18. [18] Comptes rendus de la RCP 25 du CNRS, t. 30, 1982, publication de l'Institut de Recherches Mathématiques Avancées, Université de Strasbourg. 
  19. [19] G. Julia, J. Math. Pur. Appl., t. 4, 1918, p. 47. 
  20. P. Fatou, Bull. Soc. Math. France, t. 47, 1919, p. 161; t. 48, 1920, p. 33; t. 48, 1920, p. 208. JFM47.0921.02
  21. P.J. Myrberg, J. Math. Pur. Appl., t. 41, 1962, p. 339. Zbl0106.04703MR161968
  22. H. Brolin, Arkiv För Math., t. 6, 1965, p. 103. Zbl0127.03401MR194595

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