Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Global order from local sources


Author: Charles Radin
Journal: Bull. Amer. Math. Soc. 25 (1991), 335-364
MSC (1985): Primary 47A35, 52A45, 82A55
DOI: https://doi.org/10.1090/S0273-0979-1991-16077-5
MathSciNet review: 1094191
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. M. Aizenman and E. H. Lieb, The third law of thermodynamics and the degeneracy of the ground state for lattice systems, J. Stat. Phys. 24 (1981), 279-297. MR 601698
  • 2. P. W. Anderson, Basic notions of condensed matter physics, Benjamin/Cummings, Menlo Park, 1984.
  • 3. S. Aubry, Weakly periodic structures and example, J. Phys. (Paris), Coll. C3, Supp. no. 3 50 (1989), 97-106. MR 999116
  • 4. S. Aubry, Weakly periodic structures with a singular continuous spectrum, Laboratoire Léon Brillouin, Gif-sur-Yvette, preprint, 1989. MR 999116
  • 5. R. Berger, The undecidability of the domino problem, Mem. Amer. Math. Soc., no. 66, Amer. Math. Soc., Providence, RI, 1966. MR 216954
  • 6. P. Billingsley, Ergodic theory and information, John Wiley, NY, 1965. MR 192027
  • 7. S. G. Brush, Statistical physics and the atomic theory of matter, from Boyle and Newton to Landau and Onsager, Princeton Univ. Press, Princeton, NJ, 1983, p. 277.
  • 8. J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Springer-Verlag, New York, 1988. MR 920369
  • 9. F. M. Dekking and M. Keane, Mixing properties of substitutions, Z. Wahrsch. Verw. Gebiete 42 (1978), 23-33. MR 466485
  • 10. C. Fefferman, The atomic and molecular nature of matter, Rev. Math. Iberoamericana 1 (1985), 1. MR 834355
  • 11. C. Fefferman, The N-body problem in quantum mechanics, Commun. Pure Appl. Math. Suppl. 39 (1986), S67-S109. MR 861484
  • 12. C. Gardner, J. Miękisz, C. Radin, and A. van Enter, Fractal symmetry in an Ising model, J. Phys. A.: Math. Gen. 22 (1989), L1019-1023. MR 1022124
  • 13. C F. Gauss, Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeger, Göttingische gelehrte Anzeigen, 1831 Juli 9 = Werke, II (1876), 188-196.
  • 14. J. Ginibre, Systèmes à un nombre infini de degrés de liberté, CNRS, Paris, 1969, pp. 163-175. MR 1552567
  • 15. B. Grünbaum and G. C. Shephard, Tilings and patterns, Freeman, New York, 1986. MR 992195
  • 16. G. A. Hedlund, Remarks on the work of Axel Thue on sequences, Nordisk Mat. Tidskrift 15 (1967), 148-150. MR 228875
  • 17. D. Hilbert, Mathematische Probleme, Arch. Math. Phys. 1 (1901), 44-63 and 213-237, translated in Bull. Amer. Math. Soc. 8 (1902), 437-479.
  • 18. E. H. Lieb and H.-T. Yau, The stability and instability of relativistic matter, Comm. Math. Phys. 118 (1988), 177-213. MR 956165
  • 19. E. H. Lieb and H.-T. Yau, Many-body stability implies a bound on the fine-structure constant, Phys. Rev. Letts. 61 (1988), 1695-1697. MR 961589
  • 20. M. L. Minsky, Computation: finite and infinite machines, Prentice Hall, Englewood Cliffs, NJ, 1967. MR 356580
  • 21. S. Mozes, Tilings, substitution systems and dynamical systems generated by them, J. Analyse Math. 53 (1989), 139-186. MR 1014984
  • 22. D. Myers, Nonrecursive tilings of the plane. II, J. Symbolic Logic 39 (1974), 286-294. MR 363856
  • 23. W. Parry, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc. 122 (1966), 368-378. MR 197683
  • 24. W. Parry, Topics in ergodic theory, Cambridge Tracts in Mathematics, vol. 75, Cambridge Univ. Press, London and NY, 1981, pp. 14-15. MR 614142
  • 25. R. Penrose, The role of aesthetics in pure and applied mathemtical research, Bull. Inst. Math. Appl. 10 (1974), 266-271.
  • 26. M. Queffélec, Substitution dynamical systems--spectral analysis, Lecture Notes in Math., vol. 1294, Springer-Verlag, Berlin, 1987. MR 924156
  • 27. C. Radin and L. S. Schulman, Periodicity of classical ground states, Phys. Rev. Lett. 51 (1983), 621-622. MR 714299
  • 28. C. Radin, Correlations in classical ground states, J. Stat. Phys. 43 (1986), 707-712. MR 845734
  • 29. C. Radin, Low temperature and the origin of crystalline symmetry, Internat. J. Mod. Phys. B 1 (1987), 1157-1191. MR 932349
  • 30. C. Radin, Ordering in lattice gases at low temperature, J. Phys. A: Math. Gen. 22 (1989), 317-319. MR 984765
  • 31. C. Radin, Disordered ground states of classical lattice models, Rev. Math. Phys. (to appear). MR 1121466
  • 32. F. Riesz and B. Sz-Nagy, Functional Analysis, (translated by L. F. Boron), Frederick Ungar, NY, 1955, pp. 392-393. MR 71727
  • 33. R. M. Robinson, Undecidability and nonperiodicity for tilings of the plane, Invent. Math. 12 (1971), 177-209. MR 297572
  • 34. C. A. Rogers, Packing and covering, Cambridge Univ. Press, London and NY, 1964, p. 14. MR 172183
  • 35. H. Rogers, Jr., Theory of recursive functions and effective computability, McGraw-Hill, NY, 1967. MR 224462
  • 36. D. Ruelle, Statistical mechanics; rigorous results, Benjamin, NY, 1969. MR 289084
  • 37. B. Simon, in Perspectives in mathematics: anniversary of Oberwolfach 1984, Birkhäuser Verlag, Basel, 1984, p. 442. MR 779685
  • 38. P. J. Steinhrdt and S. Ostlund, The physics of quasicrystals, World Scientific, Singapore, 1987. MR 989615
  • 39. A. Thue, Über die dichteste Zusammenstellung von kongruenten Kreisen in einer Ebene, Skr. Vidensk-Selsk., Christ., No. 1, (1910), 1-9.
  • 40. A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc., Ser. 2, 42 (1936), 230-265; 43 (1936), 544-546.
  • 41. G. E. Uhlenbeck, Statistical mechanics; foundations and applications, (T. A. Bak, ed.), Benjamin, NY, 1967, p. 581.
  • 42. G. E. Uhlenbeck, Fundamental problems in statistical mechanics. II, (E. G. D. Cohen, ed.), Wiley, NY, 1968, pp. 16-17.
  • 43. H. Wang, Proving theorems by pattern recognition. II, Bell Systs. Tech. J. 40 (1961), 1-41.
  • 44. H. Wang, Notes on a class of tiling problems, Fund. Math. 82 (1975), 295-305. MR 363854

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 47A35, 52A45, 82A55

Retrieve articles in all journals with MSC (1985): 47A35, 52A45, 82A55


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1991-16077-5

American Mathematical Society