1/d expansion for k -core percolation

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

Volumn 72, Issue 4, 2005, Pages

  Harris, A B ^a   Schwarz, J M ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; MAGNETIC SUSCEPTIBILITY; MIXTURES; MOLECULAR ORIENTATION; PHASE TRANSITIONS; PROBABILITY;

CLUSTERING PHENOMENON; DIVERGING LENGTH SCALE; K -CORE PERCOLATION;

PERCOLATION (FLUIDS);

EID: 33244476457     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.046123     Document Type: Article

References (43)

1. J. Adler, R. G. Palmer, and H. Meyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.882 58, 882 (1987).
2. S. Feng and P. N. Sen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.216 52, 216 (1984).
3. Y. Kantor and I. Webman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.1891 52, 1891 (1984).
4. S. Feng, M. F. Thorpe, and E. Garboczi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.276 31, 276 (1985).
5. A. R. Day, R. R. Tremblay, and A. M. S. Tremblay, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.2501 56, 2501 (1986).
6. Rigidity Theory and Applications, edited by, M. Thorpe, and, P. M. Duxbury, Fundamental Materials Research (Kluwer Academic/Plenum Press, New York, 1999).
7. J. M. Schwarz, A. J. Liu, and L. Q. Chayes, e-print cond-mat/0410595.
8. A. J. Liu and S. R. Nagel, Nature (London) NATUAS 0028-0836 10.1038/23819 396, 21 (1998).
9. C. S. O'Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.011306 68, 011306 (2003).
10. J. Chalupa, P. L. Leath, and G. R. Reich, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/12/1/008 12, L31 (1979).
11. B. Pittel, J. Spencer, and N. Wormald, J. Comb. Theory, Ser. B JCBTB8 0095-8956 10.1006/jctb.1996.0036 67, 111 (1996).
12. C. Moukarzel, P. M. Duxbury, and P. L. Leath, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.5800 55, 5800 (1997).
13. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1992).
14. S. Henkes and B. Chakraborty, e-print cond-mat/0504371.
15. P. M. Kogut and P. L. Leath, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/14/22/013 14, 3187 (1981).
16. J. Adler and U. Lev, Braz. J. Phys. BJPHE6 0103-9733 33, 641 (2003), and references therein.
17. M. C. Medeiros and C. M. Chaves, Physica A PHYADX 0378-4371 10.1016/S0378-4371(96)00315-9 234, 604 (1997).
18. A. C. D. van Enter, J. Stat. Phys. JSTPBS 0022-4715 48, 943 (1987).
19. Even though pc =1, recent results for a modified k=3 model on the square lattice demonstrate two new near-jammed crossover regimes as a function of occupation probability. See P. De Gregorio, A. Lawlor, P. Bradley, and K. A. Dawson, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0408756102 102, 5669 (2005).
20. C. Toninelli, G. Biroli, and D. S. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.185504 92, 185504 (2004).
21. K. G. Wilson, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.4.3174 4, 3174 (1971).
22. K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.28.240 28, 240 (1972).
23. G. Toulouse, Nuovo Cimento Soc. Ital. Fis., B NIFBAP 0369-4100 23, 234 (1974).
24. A. B. Harris and T. C. Lubensky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.35.327 35, 327 (1975);
25. A. B. Harris and T. C. Lubensky, Phys. Rev. Lett. PRLTAO 0031-9007 35, 1397 (1975).
26. M. E. Fisher and D. S. Gaunt, Phys. Rev. PRVAAH 0096-8250 10.1103/PhysRev.133.A224 133, A224 (1964).
27. R. R. P. Singh and M. E. Fisher, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.340575 63, 3994 (1988).
28. A. B. Harris, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.26.337 26, 337 (1982).
29. D. S. Gaunt and H. Ruskin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/11/7/025 11, 1369 (1978).
30. G. A. Baker, Jr. and L. P. Benofy, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01011786 29, 699 (1982).
31. S. Wolfram, The Mathematica Book, Version 4, 4th ed. (Cambridge University Press, New York, 1999).
32. A. B. Harris and T. C. Lubensky, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/16/11/005 16, L365 (1983);
33. A. B. Harris, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.2614 28, 2614 (1983).
34. N. S. Branco and C. J. Silva, Int. J. Mod. Phys. C IJMPEO 0129-1831 10, 921 (1999).
35. T. C. Lubensky and J. Isaacson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.20.2130 20, 2130 (1979).
36. S. P. Obukhov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74. 4472 74, 4472 (1995).
37. H. Ji and M. O. Robbins, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.14519 46, 14519 (1992).
38. T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.36.8552 36, 8552 (1986).
39. E. Donth, The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials (Springer, New York, 2001).
40. G. H. Fredrickson and H. C. Andersen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.1244 53, 1244 (1984).
41. F. Ritort and P. Sollich, Adv. Phys. ADPHAH 0001-8732 10.1080/0001873031000093582 52, 219 (2003).
42. M. Sellitto, G. Biroli, and C. Toninelli, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10372-5 69, 496 (2005).
43. K. F. Kelton, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 195504 90, 195504 (2003).