Square lattice Ising model susceptibility: Series expansion method and differential equation for χ(3)

Journal of Physics A: Mathematical and General

Volumn 38, Issue 9, 2005, Pages 1875-1899

  Zenine, N ^a   Boukraa, S ^b   Hassani, S ^a   Maillard, J M ^c  

^a CENTRE DE RECHERCHE NUCLÉAIRE D ALGER   (Algeria)

^b UNIVERSITY OF BLIDA   (Algeria)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14844320097     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/9/004     Document Type: Article

References (55)

1. Wu T T, McCoy B M, Tracy C A and Barouch E 1976 Phys. Rev. B 13 316-74
2. Nappi C R 1978 Nuovo Cimento A 44 392
3. Palmer J and Tracy C 1981 Adv. Appl. Math. 2 329
4. Yamada K 1984 Prog. Theor. Phys. 71 1416
5. Yamada K 1985 Phys. Lett. A 112 456-8
6. Nickel B 1999 J. Phys. A: Math. Gen. 32 3889-906
7. Nickel B 2000 J. Phys. A: Math. Gen. 33 1693-711
8. Zenine N, Boukraa S, Hassani S and Maillard J M 2004 J. Phys. A: Math. Gen. 37 9651-68 (Preprint math-ph/0407060)
9. Syozi I and Naya S 1960 Prog. Theor. Phys. 24 829
10. Hansel D and Maillard J-M 1988 J. Phys. A: Math. Gen. 21 213-25
11. Dhar D and Maillard J-M 1985 J. Phys. A: Math. Gen. 18 L383-8
12. Baxter R J 1982 J. Stat. Phys. 28 1-41
13. Jaekel M T and Maillard J-M 1985 J. Phys. A: Math. Gen. 18 641, 1229, 2271
14. Hansel D and Maillard J-M 1987 Mod. Phys. Lett. B 1145-53
15. Hansel D and Maillard J-M 1988 Int. J. Mod. Phys. B 2 1447-62
16. Yang C N 1952 Phys. Rev. 85 808-16
17. Chang C H 1952 Phys. Rev. 88 1422
18. Hansel D, Maillard J M, Oitmaa J and Vergakis M J 1987 J. Stat. Phys. 48 69-80
19. Guttman A J and Enting I G 1996 Phys. Rev. Lett. 76 344-7
20. Lipshitz L 1989 J. Algebra 122 354
21. Zeilberger D 1990 J. Comput. Appl. Math. 32 321
22. Cartier P 2002 Fonctions polylogarithmes, nombres polyzétas et groupes pro-unipotents Astérisque 282 137-73 (Sém. Bourbaki no 885)
23. Terasoma T 2002 Invent. Math. 149 339-69 (Preprint AG/0104231)
24. Hoffman M E and Ohno Y 2003 J. Algebra 262 332-47 (Preprint QA/0010140)
25. Oi S 2004 Representation of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta values Preprint NT/0405162
26. Ince H K 1927/1956 Ordinary Differential Equations (London/New York: Longmans/Dover)
27. Mugan U and Sakka A 1995 J. Math. Phys. 36 1284-98
28. Painlevé P 1900 Bull. Soc. Math. Phys. France 28 201-61
29. Kitaev A V 2001 Special functions of the isomonodromy type, rational transformations of spectral parameter, and algebraic solutions of the sixth Painlevé equation Preprint nlin/0102020
30. Barouch E, McCoy B M and Wu T T 1973 Phys. Rev. Lett. 31 1409-11
31. Chazy J 1910 C. R. Acad. Sci., Paris 150 456-8
32. Chazy J 1911 Acta Math. 34 317-85
33. Conte R The Painlevé Property, One Century Later (CRM Series in Mathematical Physics) ed R Conte (Berlin: Springer)
34. Kruskal M D, Joshi N and Halburd R 1997 Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property Integrability of Nonlinear Systems (Pondicherry, India) (Lecture Notes in Physics vol 495) ed B Grammaticos and K Tamizhmani (Berlin: Springer) pp 171-205
35. Orrick W P, Nickel B G, Guttmann A J and Perk J H H 2001 J. Stat. Phys. 102 795-841
36. Orrick W P, Nickel B G, Guttmann A J and Perk J H H 2001 Phys. Rev. Lett. 86 4120-3
37. McCoy B M and Wu T T 1980 Phys. Rev. Lett. 45 675-8
38. Perk J H H 1980 Phys. Lett. A 79 3-5
39. Jimbo M and Miwa T 1980 Proc. Japan Acad. A 56 405 Jimbo M and Miwa T 1981 Proc. Japan Acad. A 57 347
40. Jimbo M and Miwa T 1980 Proc. Japan Acad. A 56 405 Jimbo M and Miwa T 1981 Proc. Japan Acad. A 57 347
41. McCoy B M and Wu T T 1981 Nucl. Phys. B 180 89
42. Rehr J J, Joyce G S and Guttmann A J 1980 J. Phys. A: Math. Gen. 13 1587-602
43. Khan M H 2002 J. Comput. Appl. Math. 149 457-68
44. Sasaki T 2001 Kyushu J. Math. 55 1-21
45. Higashi K and Sasaki T 2004 Kyushu J. Math. 58 105-20
46. Sasaki T and Yoshida M 2001 J. Phys. A: Math. Gen. 34 2319-28
47. Sasaki T and Yoshida M 1999 Proc. Japan Acad. 75 129-33
48. Sasaki T and Yoshida M 2000 Kobe J. Math. 17 29-57
49. Maillard J M 1995 Math. Comput. Modelling 26 169-225
50. Boukraa S, Maillard J-M and Rollet G 1995 J. Stat. Phys. 78 1195-251
51. Boukraa S and Maillard J-M 2001 J. Stat. Phys. 102 641-700 (Preprint hep-th/0003212)
52. Gasper G 1990 Using symbolic computer algebraic systems to derive formulae involving orthogonal polynomials and other special functions Orthogonal Polynomials: Theory and Practice ed P Nevai (Boston, MA: Kluwer) pp 163-79
53. Avan J, Maillard J-M, Talon M and Viallet C-M 1990 Int. J. Mod. Phys. B 4 1895-912
54. Gomez C, Ruiz-Altaba M and Sierra G 1996 Duality in conformal field theories Quantum Groups in Two-dimensional Physics (Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press) chapter 9
55. Mgfun's project: http://algo.inria.fr/chyzak/mgfun.html; gfun (generating functions package): http://algo.inria.fr/libraries