Problèmes combinatoires posés par la physique statistique

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1. [1] R. Baxter, Exactly solved models in statistical mechanics, Academic Press, New-York, 1982. Des livres de base sur la mécanique statistique sont : Zbl0723.60120MR690578
2. [2] D. Ruelle, Statistical mechanics, rigorous results, Benjamin, New-York, 1969, Zbl0177.57301MR289084
3. [3] C. Domb et M.S. Green, eds, Phase transition and critical phenomena, Academic Press, New-York, 1974. Pour les méthodes combinatoires en physique statistique, une solution combinatoire du modèle d'Ising et une formulation dans le langage des graphes, voir respectivement MR353911
4. [4] J.K. Percus, Combinatorial methods, Applied mathematical sciences, vol. 4, Springer-Verlag, New-York/Berlin, 1971, Zbl0268.05003MR345825
5. [5] P.W. Kasteleyn, Graph theory and crystal physics, in "Graph theory and theoretical physics", F. Harary ed., Academic Press, New-York, 1967, 43-110, Zbl0205.28402MR253689
6. [6] F.Y. Wu, Graph theory in statistical physics, in "Studies in foundations and combinatorics", Advances in Math. supplementary studies, vol. 1, 1978. Pour une revue très récente des problèmes de percolation, percolation dirigée et animaux voir (avec les articles de synthèse cités) Zbl0435.05061MR520558
7. [7] M. Sahimi, Critical exponents and thresholds for percolation and conduction, in "The mathematics and physics of disordered media", Lecture Notes in Maths n° 1035, Springer-Verlag, New-York/Berlin (1983), 314-346. Zbl0532.60100
8. [8] N. Breuer, Corrections to scaling for directed branched polymers (lattice animals), preprint (1983), soumis à Z. Physik B. 
9. [9] N. Breuer et H.K. Janssen, Critical behaviour of directed branched polymers and the dynamics at the Yang-Lee edge singularity, Z. Physik B, 48 (1982) 347-350. 
10. [10] J.L. Cardy, Directed lattice animals and the Lee-Yang edge singularity, J. Phys. A : Math. Gen., 15 (1982),L593-L595. MR679087
11. [11] A.R. Day et T.C. Lubensky, ε expansion for directed animals, J. Phys. A : Math. Gen., 15 (1982),L 285-L 290. 
12. [12] D. Dhar, Equivalence of the two-dimensional directed-site animal problem to Baxter's Hard-Square Lattice-Gas model, Phys. Rev. Lett., 49 (1982), 959-962. MR675054
13. [13] D. Dhar, Exact solution of a directed-site animals-enumeration problem in 3 dimensions, Phys. Rev. Lett., 59 (1983), 853-856. MR721768
14. [14] D. Dhar, M.K. Phani et M. Barma, Enumeration of directed site animals on two-dimensional lattices, J. Phys. A : Math. Gen., 15 (1982), L 279-L 284. MR663685
15. [15] F. Family, Relation between size and shape of isotropic and directed percolation clusters and lattice animals,J. Phys. A : Math. Gen., 15 (1982), L583-L 592. MR679086
16. [16] J.E. Green et M.A. Moore, Application of directed lattice animal theory to river networks, J. Phys. A : Math. Gen., 15 (1982), L 597-L 599. MR679088
17. [17] V. Hakim et J.P. Nadal, Exact results for 2 D directed animals on a strip of finite width, J. Phys. A : Math. Gen., 16 (1983), L 213-L 218. MR707373
18. [18] H. Herrmann, F. Family et H.E. Stanley, Position-space renormalisation group for directed branched polymers, J. Phys. A : Math. Gen., 16 (1983), L 375-L 379. 
19. [19] T.C. Lubensky et J. Vannimenus, Flory approximation for directed branched polymers and directed percolation, J. Physique, 43 (1982), L 377-L381. 
20. [20] J.P. Nadal, Etude de systèmes dirigés en physique statistique, Thèse 3ème cycle, Univ. d'Orsay, 1983. 
21. [21] J.P. Nadal, B. Derrida et J. Vannimenus, Directed lattice animals in 2 dimensions : numerical and exact results, J. Physique, 43 (1982), 1561. MR684783
22. [22] J.P. Nadal, B. Derrida et J. Vannimenus, Directed Diffusion-controlled Aggregation versus directed animals, Preprint (1983). 
23. [23] S. Redner et A. Conioeio, Flory theory for directed lattice animals and directed percolation, J. Phys. A : Math. Gen., 15 (1982, L 273 -L 278. 
24. [24] S. Redner et Z.R. Yang, Size and shape of directed lattice animals, J. Phys. A : Math. Gen., 15 (1982), L177 - L187. MR655343
25. [25] H.E. Stanley , S. Redner et Z.R. Yang, Site and bond directed branched polymers for arbitrary dimensionality : evidence supporting a relation with the Lee-Yang edge arbitrary, J. Phys. A : Math. Gen., 15 (1982), L569 -L573. MR684576
26. [26] G. Viennot, Combinatorial solution of the 2D directed lattice animals problem with heaps of dominos, en préparation. 
27. [27] G. Viennot, Directed animals and combinatorial interpretation of the density of a gaz, destiné à Advances in Applied Maths. 
28. [28] G. Viennot et D. Gouyou-Beauchamps, The number of directed animals, destiné à Advances in Maths. Zbl0727.05036
29. [29] G.E. Andrews, R.J. Baxter et P.J. Forresters, Eight vertex SOAS model and generalized Rogers-Ramanujan type identities, preprint (1984). MR748075
30. [30] R.J. Baxter, Hard hexagons : exact solution, J. Phys. A : Math. Gen.13 (1980)L61 -L70. MR560533
31. [31] R.J. Baxfer, Rogers-Ramanujan identities in the hard hexagon model, J. Stat. Physics, 26 (1981), 427-452. Zbl0511.05004MR648195
32. [32] R.J. Baxter, Lettre à Dhar, citée dans [12]. 
33. [33] R.J. Baxter et P.A. Pearce, Hard hexagones : interfacial tension and correlation length, J. Phys. A : Math. Gen., 15 (1982), 897-910. MR653418
34. [34] M.T. Jaekel et J.M. Mkillard, Modèles solubles en mécanique statistique, Proc. R.C.P.25, vol.29, Publ. IRMA, Strasbourg (1982),93. 
35. [35] J.M. Maillard, Equations fonctionnelles en mécanique statistique, Note CEA-N- 2332, (1983). 
36. [36] G. Parisi et N. Sourlas, Phys. Rev. Lett.14 (1981), 871. Zbl0969.82030MR609853
37. [37] A.M.W. Verhagen, J. Stat. Phys., 15 (1976), 219. MR428999
38. [38] P. Cartier et D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Maths. n°85, Springer-Verlag, New-York/Berlin, 1969. Zbl0186.30101MR239978
39. [39] M. de Sainte Catherine, Couplage et Pfaffien en combinatoire et physique, Thèse 3ème cycle, Université de Bordeaux I, 1983. 
40. [40] S. Dulucq et G. Viennot, The Cartier-Foata commutation monoid revisited with heaps of pieces, manuscrit, 1983. 
41. [41] D. Dumont, Une approche combinatoire des fonctions elliptiques de Jacobi, Advances in Maths., 41 (1981), 1-39. Zbl0483.33001MR625332
42. [42] P. Flajolet, Combinatorial aspects of continued fractions, Discrete Math., 32 (1980) , 125-161. Zbl0445.05014MR592851
43. [43] D. Foata, La série génératrice exponentielle dans les problèmes d'énumération, Presses de l'Univ. de Montréal, (1974). Zbl0325.05007MR505546
44. [44] D. Foata, A non-commutative version of the matrix inversion formula, Advances in Maths., 31 (1979), 330-349. Zbl0418.15004MR532839
45. [45 ] D. Foata, A combinatorial proof of Jacobi's identity, Annals of Discrete Maths.6 (1980) , 125-135. Zbl0448.05006MR593527
46. [46] D. Foata, M.P. Schützenberger, Théorie géométrique des polynômes Eulériens, Lecture Notes in Maths. n°138, Springer-Verlag, New-York/Berlin, (1970). Zbl0214.26202MR272642
47. [47] A. Garsia, S. Milne, A Rogers-Ramanujan bijection, J. Combinatorial Th., A, 31 (1981), 289-339. Zbl0477.05009MR635372
48. [48] C.D. Godsil, Matchings and walks in graphs, J. Graphs Th., 5 (1981), 285-291. Zbl0466.05053MR625070
49. [49] S.N. Joni et G.C. Rota, Coalgebras and bialgebras in combinatorics, Studies in Applied Maths., 61 (1979), 93-139. Zbl0471.05020MR544721
50. [50 ] A. Joyal, Une théorie combinatoire des séries formelles, Advances in Maths., 42, (1981), 1-82. Zbl0491.05007MR633783
51. [51 ] P.A. Macmahon, Combinatory Analysis, Cambridge Univ. Press, London, 1915. Réimpression Chelsea, New-York, (1960). Zbl46.0118.07MR141605JFM46.0118.07
52. [52] G.C. Rota, On the foundations of combinatorial theory, I. Theory of Möbius functions, Z. Wahrsch. Band 2, Heft 4, (1964), 340-368. Zbl0121.02406MR174487
53. [53 ] G. Viennot, Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi, J. Combinatorial Th. A, 29 (1980), 121-133. Zbl0444.33002MR583951
54. [54 ] G. Viennot, Théorie combinatoire des nombres d'Euler et Genocchi, Séminaire Théorie des Nombres1981/82, Publication Université de Bordeaux I, 94 p. 
55. [55] G. Viennot, Théorie combinatoire des polynômes orthogonaux généraux, Notes de séminaire de l'Univ. du Québec à Montréal, (1983), 165 p. 
56. [56] G.E. Andrews, The theory of partitions, Encyclopedia of Maths. and its applications, G.C. Rota ed., vol.2, Addison-Wesley, Reading, (1976). Zbl0655.10001MR557013
57. [57] G.E. Andrews, The hard-hexagon model and Rogers-Ramanujan identities, Proc. Nat. Acad. Sci. U.S.A., 78, (1981), 5290-5292. Zbl0526.33004MR629656
58. [58] P. Cartier, La théorie classique et moderne des fonctions symétriques, Séminaire Bourbaki, exposé n°597, Astérisque n°105-106, (1983), 1-23. Zbl0534.20005MR728978
59. [59] I.G. Macdonald, Affine Lie algebras and modular forms, Séminaire Bourbaki, exposé n°577, Lecture Notes in Maths. n°901, Springer-Verlag, Berlin/ New-York, (1981), 258-275. Zbl0472.17006MR647501

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