Rigidity percolation in a field

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 5 2, 2003, Pages 561041-5610416

  Moukarzel, Cristian F ^a  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); ENTROPY; EQUATIONS OF STATE; FREE ENERGY; GRAPH THEORY; MAGNETIC PROPERTIES; MATHEMATICAL MODELS; PROBLEM SOLVING; RANDOM PROCESSES; SPECIFIC HEAT;

BOOTSTRAP PERCOLATION; RIGIDITY PERCOLATION;

PHASE TRANSITIONS;

EID: 0942289355     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (68)

1. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, Bristol, 1994).
2. Fractals and Disordered Systems, 2nd ed., edited by A. Bunde and S. Havlin (Springer-Verlag, Heidelberg, 1996).
3. A. Coniglio and W. Klein, J. Phys. A 13, 2775 (1980).
4. W. Klein and A. Coniglio, Phys. Lett. A 84, 83 (1981).
5. A. Coniglio and F. Peruggi, J. Phys. A 15, 1873 (1982).
6. M. Sahimi, Applications of Percolation Theory, 1st ed. (Taylor and Francis, Bristol, 1994).
7. M. Sahimi, Phys. Rep., Phys. Lett. 306, 214 (1998).
8. S. Feng and P. Sen, Phys. Rev. Lett. 52, 216 (1984).
9. Y. Kantor and I. Webman, Phys. Rev. Lett. 52, 1891 (1984).
10. S. Feng, M. Thorpe, and E. Garboczi, Phys. Rev. B 31, 276 (1985).
11. M.F. Thorpe, J. Non-Cryst. Solids 76, 109 (1985).
12. A. Day, R. Tremblay, and A. Tremblay, Phys. Rev. Lett. 56, 2501 (1986).
13. M. Thorpe and E. Garboczi, Phys. Rev. B 35, 8579 (1987).
14. Rigidity Theory and Applications, edited by M. Thorpe and P. M. Duxbury, Fundamental Materials Research (Kluwer Academic, Dordrecht/Plenum Press, New York, 1999).
15. C. Moukarzel and P. Duxbury, Phys. Rev. E 59, 2614 (1999).
16. H. Crapo, Struct. Topol. 1, 26 (1979).
17. W. Whiteley, Trans. Am. Math. Soc. 285, 431 (1984).
18. B. Hendrickson, SIAM J. Comput. 21, 65 (1992).
19. See Refs. [8,9,15,48], and also C. Moukarzel and P. Duxbury, in Rigidity Theory and Application (Ref. [14]).
20. C. Moukarzel, P. Duxbury, and P. Leath, Phys. Rev. E 55, 5800 (1997).
21. P. Duxbury, D. Jacobs, M. Thorpe, and C. Moukarzel, Phys. Rev. E 59, 2084 (1999).
22. F.Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
23. B. Bollobas, G. Grimmett, and S. Janson, Probab. Theory Relat. Fields 104, 283 (1996).
24. F. Karsch, C. Schmidt, and S. Stickan, Comput. Phys. Commun. 147, 451 (2002).
25. H. Satz, Comput. Phys. Commun. 147, 46 (2002).
26. S. Fortunato, J. Phys. A 36, 4269 (2003).
27. F. Karsch and S. Stickan, Phys. Lett. B 488, 319 (2000).
28. S. Fortunato and H. Satz, Nucl. Phys. B, Proc. Suppl. 106, 890 (2002).
29. S. Kirkpatrick, Phys. Rev. Lett. 36, 69 (1976).
30. M. Giri, M. Stephen, and G. Grest, Phys. Rev. B 16, 4971 (1977).
31. M.J. Stephen, Phys. Rev. B 15, 5674 (1977).
32. P. Reynolds, H. Stanley, and W. Klein, J. Phys. A 11, L199 (1978).
33. H. Nakanishi and P. Reynolds, Phys. Lett. A 71, 252 (1979).
34. J.W. Essam, Rep. Prog. Phys. 43, 833 (1980).
35. P. Reynolds, H. Stanley, and W. Klein, Phys. Rev. B 21, 1223 (1980).
36. J. Chalupa, P.L. Leath, and G.R. Reich, J. Phys. C 12, L31 (1979).
37. J. Adler, Physica A 171, 453 (1991).
38. M. Kaufman and D. Stauffer, J. Stat. Phys. 73, 843 (1993).
39. M. de Menezes and C. Moukarzel, Phys. Rev. E 60, 5699 (1999).
40. B. Bollobás, in Graph Theory and Combinatorics, Proceedings of the Cambridge Combinatorial Conference in honor of Paul Erdös. edited by B. Bollobás (Academic Press, New York, 1984), pp. 35-57.
41. T. Luczak, Discrete Math. 91, 61 (1991).
42. M. Molloy, Random Struct. Algorithms 8, 159 (1996).
43. B. Pittel, J. Spencer, and N. Wormald, J. Comb. Theory, Ser. B 67, 111 (1996).
44. However, the rigid cluster is not a subset of the (g + 1) core.
45. B. Bollobás, Random Graphs, 2nd ed. (Cambridge University Press, Cambridge, 2001).
46. P. Kasteleyn and C. Fortuin, J. Phys. Soc. Jpn. S26, 11 (1969).
47. C. Fortuin and P. Kasteleyn, Physica 57, 536 (1972).
48. D. Jacobs and M. Thorpe, Phys. Rev. E 53, 3682 (1996).
49. For a discussion see, for example, Ref. [50].
50. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, International Series of Monographs on Physics (Oxford University Press, Oxford, 1987).
51. C. Moukarzel, J. Phys. A 29, 8079 (1996).
52. D. Jacobs and M. Thorpe, Phys. Rev. Lett. 75, 4051 (1995).
53. C. Moukarzel (unpublished).
54. This rigid background plays the role of the ghost site in SP.
55. S. Cannas, A. de Magalhaes, and F. Tamarit, Phys. Rev. B 61, 11 521 (2000).
56. 1 does not have zero second derivative at the critical point.
57. Or zero modes, or floppy modes.
58. For alternative derivations, see Refs. [21,48].
59. J.J. Binney, N.J. Dowrick, A.J. Fisher, and M.E.J. Newman, The Theory of Critical Phenomena: An Introduction to the Renormalization Group (Oxford University Press, New York, 2002).
60. D.A. Lavis and G.M. Bell, Statistical Mechanics of Lattice Systems, Texts and Monographs in Physics (Springer-Verlag, Berlin, 1999).
61. K. Huang, Statistical Mechanics, 2nd ed. (Wiley, New York, 1987).
62. M. Biskup and L. Chayes, Commun. Math. Phys (to be published), e-print math.PR/0207242.
63. C. Moukarzel and P. Duxbury, Phys. Rev. Lett. 75, 4055 (1995).
64. G.G. Naumis, Phys. Rev. B 61, R9205 (2000).
65. J.C. Phillips, J. Non-Cryst. Solids 34, 153 (1979).
66. J. Phillips and M. Thorpe, Solid State Commun. 53, 699 (1985).
67. A. Coniglio, J. Phys. A 15, 3829 (1982).
68. D. Jacobs and B. Hendrickson, J. Comput. Phys. 137, 346 (1997).