Random tilings of high symmetry: I. Mean-field theory

Journal of Statistical Physics

Volumn 120, Issue 5-6, 2005, Pages 799-835

  Destainville, N ^a   Widom, M ^b   Mosseri, R ^c   Bailly, F ^a  

^a CNRS   (France)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

Entropy; Mean field theory; Quasicrystal; Random tiling

Indexed keywords

EID: 27844528345     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-6989-y     Document Type: Article

References (63)

1. D. Shechtman, et al., Phys. Rev. Lett. 53:1951 (1984).
2. D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53:2477 (1984).
3. R. Penrose, Bull Inst. Math. Appl. 10:226 (1974).
4. V. Elser, Phys. Rev. Lett. 54:1730 (1985).
5. C. L. Henley, in D. P. Di Vincenzo and P. J. Steinhart eds. Quasicrystals, the State of the Art (World Scientific, 1991), p. 429.
6. M. Widom, K. J. Strandburg, and R. H. Swendsen, Phys. Rev. Lett. 58:706 (1987).
7. F. Lançon, L. Billard and P. Chaudhari, Europhys. Lett. 2:625 (1986).
8. H.-C. Jeong and P. J. Steinhardt, Phys. Rev. Lett. 73:1943 (1994);
9. K. Ingersent and P. J. Steinhardt, Phys. Rev. Lett., 64:2034 (1990).
10. M. Widom, in M.V. Jaric and S. Lundqvist eds. Quasicrystals (World Scientific, 1990), p. 337.
11. R. Mosseri and F. Bailly, Int. J. Mod. Phys. B 6&7:1427 (1993).
12. N. Destainville, R. Mosseri, and F. Bailly, J. Stat. Phys. 87:697 (1997).
13. N. Destainville, R. Mosseri, and F. Bailly, J. Stat. Phys. 102:147 (2001).
14. A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. M. Ziegler Oriented Matraids, (Cambridge University Press, 1993).
15. R. Kenyon, Algorithmica 9:382 (1993).
16. S. Elnitsky, J. Combinatorial Theory A 77:193-221 (1997).
17. G. D. Bailey, Tilings of Zonotopes: Discriminental Arrangements, Oriented Matroids, and Enumeration, Ph. D. Thesis (University of Minnesota, 1997).
18. H. Cohn, M. Larsen, and J. Propp, New York J. of Math. 4:137 (1998).
19. H. Cohn, R. Kenyon, and J. Propp, J. of the AMS 14:297 (2001).
20. R. Cerf and R. Kenyon, Comm. Math. Phys. 222:147 (2001).
21. M. Latapy, RAIRO-Theor. Inf. Appl. 36:389 (2002).
22. H. W. J. Blöte and H.J. Hilhorst, J. Phys. A: Math. Gen. 15:L631 (1982).
23. M. Widom Phys. Rev. Lett. 70:2094 (1993);
24. P. Kalugin J. Phys. A: Math. Gen. 27:3599 (1994);
25. J. de Gier, B. Nienhuis, Phys. Rev. Lett. 76:2918 (1996);
26. J. de Gier and B. Nienhuis, J. Phys. A: Math. Gen. 31:2141 (1998).
27. B. Nienhuis, Phys. Rep. 301:271 (1998).
28. D. M. Knuth, Axioms and Hulls, Lect. Notes in Computer Sci. 606:35 (1992).
29. M. Widom, N. Destainville, R. Mosseri, and F. Bailly, in Proceedings of the 6th International Conference on Quasicrystals, (World Scientific, Singapore, 1997).
30. M. V. Jaric and S. L. Johnson, Phys. Lett. A 219:238 (1996);
31. C. Zeng, J. Kondev, D. McNamara and A.A. Middleton, Phys. Rev. Lett. 80:109 (1998).
32. K. J. Strandburg, L.-H. Tang and M. V. Jaric Phys. Rev. Lett. 63:314 (1989);
33. L. J. Shaw, V. Elser, and C. L. Henley, Phys. Rev. B 43:3423 (1989);
34. L.-H. Tang, Phys. Rev. Lett. 64:2390 (1990);
35. M. Oxborrow and C. L. Henley, Phys. Rev. B 48:6966 (1993);
36. F. Gahler, Proc. ICQ5 236 (1995);
37. D. Joseph and M. Baake, J. Phys. A 29:6709 (1996).
38. M. Widom, D. P. Deng and C. L. Henley, Phys. Rev. Lett. 63:310 (1989);
39. L. J. Shaw and C. L. Henley, J. Phys. A 24:4129 (1991);
40. M.E.J. Newman and C. L. Henley, Phys. Rev. B 52:6386 (1995).
41. C. Itzykson, J.-M. Drouffe, Statistical Field Theory, Vol. 1 (Cambridge Monographs on Mathematical Physics, 1992).
42. V. E. Korepin, F. Gahler and J. Rhyner, Acta Cryst. A 44:667 (1988).
43. J. E. S. Socolar, P.J. Steinhardt and D. Levine, Phys. Rev. B 32:5547 (1985).
44. D. A. Rabson, N. D. Mermin, D. S. Rokhsar and D. C. Wright, Rev. Mod Phys. 63:699 (1991).
45. B. Bollobas Random graphs (Academic Press, New York, 1985).
46. J. Vidal, N. Destainville, and R. Mosseri, Phys. Rev. B 68:172202 (2003).
47. N. Destainville, M. Widom, R. Mosseri, and F. Bailly, Mat. Sci. Eng. A 294:409 (2000).
48. M. Widom, N. Destainville, R. Mosseri, and F. Bailly, Random tilings with high symmetry: II. Boundary conditions and numerical studies, J. Stat. Phys. 120(5/6):837-873 (2005).
49. V. Elser, J. Phys. A 17:1509 (1984).
50. G. H. Wannier, Phys. Rev. 79:357 (1950);
51. Phys. Rev. B 7:5017 (E 1973).
52. N. Destainville, J. Phys. A: Math. Gen 31:6123 (1998).
53. H. S. M. Coxeter, Regular Polytopes (Dover, 1973).
54. V. Desoutter, N. Destainville, J. Phys. A: Math. Gen. 38:17 (2005).
55. W. Li, H. Park, and M. Widom, J. Stat. Phys. 66:1 (1992).
56. N. G. de Bruijn, Ned. Akad. Wetensch. Proc. A 84:39 (1981);
57. J. Phys. France 47:C3-9 (1986).
58. J. E. S. Socolar, P. J. Steinhardt and D. Levine, Phys. Rev. B 32(8):5547 (1985).
59. F. Gähler and J. Rhyner, J. Phys. A: Math. Gen. 19:267 (1986).
60. C. L. Henley, J. Phys. A: Math. Gen. 21:1649 (1988).
61. M. E. Fisher, J. Stat. Phys. 34:667 (1984).
62. M. Widom, R. Mosseri, N. Destainville, F. Bailly, J. Stat. Phys. 109:945 (2002).
63. K. J. Standburg, Phys. Rev. B 44:4644 (1991).