Minimum spanning trees and random resistor networks in d dimensions

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

Volumn 72, Issue 3, 2005, Pages

  Read, N ^a  

^a Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MINIMUM SPANNING TREES; PERCOLATION; RANDOM RESISTOR NETWORKS; SCALING RELATION;

ALGORITHMS; BOUNDARY CONDITIONS; MATHEMATICAL MODELS; OPTIMIZATION; RESISTORS; TRAVELING SALESMAN PROBLEM; TREES (MATHEMATICS);

RANDOM PROCESSES;

EID: 28844436887     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.036114     Document Type: Article

References (71)

1. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity (Dover, Mineola, NY, 1998), Chap..
2. J. M. Steele, Probability Theory and Combinatorial Optimization (SIAM, Philadelphia, PA, 1997).
3. Spin Glass Theory and Beyond, edited by, M. Mezard, G. Parisi, and, M. Virasoro, (World Scientific, Singapore, 1987).
4. C. M. Newman and D. L. Stein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.2286 72, 2286 (1994).
5. P. Jaillet, Oper. Res. Lett. ORLED5 0167-6377 10.1016/0167-6377(93)90098-2 14, 73 (1993).
6. J. B. Kruskal, Proc. Am. Math. Soc. PAMYAR 0002-9939 7, 48 (1956).
7. A. J. Bray and M. A. Moore, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/18/004 17, L463 (1984);
8. A. J. Bray and M. A. Moore, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.631 31, 631 (1985);
9. W. L. McMillan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.340 31, 340 (1985);
10. W. L. McMillan, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/17/18/010 17, 3179 (1984);
11. D. S. Fisher and D. A. Huse, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.1601 56, 1601 (1986);
12. D. S. Fisher and D. A. Huse, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.386 38, 386 (1988).
13. J. P. Bouchaud, F. Krzakala, and O. C. Martin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.224404 68, 224404 (2003).
14. M. A. Moore, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.1703 58, 1703 (1987).
15. J. L. Jacobsen, N. Read, and H. Saleur, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.038701 93, 038701 (2004).
16. D. Aldous and A. G. Percus, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.1635191100 100, 11211 (2003).
17. M. Aizenman, A. Burchard, C. M. Newman, and D. B. Wilson, Random Struct. Algorithms RSALFD 1042-9832 10.1002/(SICI)1098-2418(199910/12)15:3/4<319::AID-RSA8>3.3.CO;2-7 15, 319 (1999).
18. N. Read, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.027103 70, 027103 (2004).
19. R. Pemantle, Ann. Prob. APBYAE 19, 1559 (1991).
20. J. H. van Lint and R. M. Wilson, A Course in Combinatorics (Cambridge University, Cambridge, 1992), Chap..
21. F. J. Dyson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.92.1331 92, 1331 (1953).
22. S. John, H. Sompolinsky, and M. J. Stephen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.27.5592 27, 5592 (1983).
23. T. A. L. Ziman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.337 49, 337 (1982).
24. V. Gurarie and J. T. Chalker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.134207 68, 134207 (2003).
25. D. Stauffer and A. Aharony, Introduction to Percolation Theory 2nd ed. (Taylor and Francis, London, 1994).
26. V. Ambegaokar, B. I. Halperin, and J. S. Langer, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.4.2612 4, 2612 (1971).
27. E. Charlaix, E. Guyon, and S. Roux, Transp. Porous Media TPMEEI 0169-3913 2, 31 (1987);
28. S. Tyč and B. I. Halperin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.877 39, 877 (1989).
29. P. Le Doussal, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.881 39, 881 (1989).
30. Z. Wu, e-print cond-mat/0411062.
31. M. Cieplak, A. Maritan, and J. R. Banavar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.2320 72, 2320 (1994).
32. A.-L. Barabási, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.3750 76, 3750 (1996).
33. M. Cieplak, A. Maritan, and J. R. Banavar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.3754 76, 3754 (1996).
34. R. Dobrin and P. M. Duxbury, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5076 86, 5076 (2001).
35. R. C. Prim, Bell Syst. Tech. J. BSTJAN 0005-8580 36, 1389 (1957);
36. E. W. Dijkstra, Numer. Math. NUMMA7 0029-599X 10.1007/BF01386390 1, 269 (1959).
37. R. Lenormand and S. Bories, Comptes Rendues Acad. Sci. CASCFN 1387-1609 291, 279 (1980);
38. R. Chandler, J. Koplick, K. Lerman, and J. F. Willemsen, J. Fluid Mech. JFLSA7 0022-1120 119, 249 (1982);
39. D. Wilkinson and J. F. Willemsen, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/16/14/028 16, 3365 (1983).
40. T. C. Hu, Oper. Res. OPREAI 0030-364X 9, 898 (1961).
41. M. Aizenman, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(96) 00626-8 485, 551 (1997).
42. P. W. Anderson, B. I. Halperin, and C. M. Varma, Philos. Mag. PHMAA4 0031-8086 25, 1 (1972);
43. W. A. Phillips, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00660072 7, 351 (1972).
44. A. A. Middleton, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.14787 61, 14787 (2000).
45. B. Wieland and D. B. Wilson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.056101 68, 056101 (2003);
46. D. B. Wilson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.037105 69, 037105 (2004).
47. A. M. Frieze, Discrete Appl. Math. DAMADU 0166-218X 10.1016/0166-218X(85)90058-7 10, 47 (1985).
48. M. E. Fisher and M. N. Barber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.28.1516 28, 1516 (1972).
49. K. Binder, M. Nauenberg, V. Privman, and A. P. Young, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.1498 31, 1498 (1985).
50. E. Brezin and J. Zinn-Justin, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(85)90379-7 257, 867 (1985).
51. C. Borgs, J. T. Chayes, H. Kesten, and J. Spencer, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s002200100521 224, 153 (2001).
52. A. B. Harris, T. C. Lubensky, W. K. Holcomb, and C. Dasgupta, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.35.327 35, 327 (1975).
53. J. L. Jones and A. P. Young, e-print cond-mat/0412150.
54. B. Bollobás, Random Graphs (Cambridge University Press, Cambridge, England, 2001).
55. E. Lawler, Combinatorial Optimization: Networks and Matroids (Dover, Mineola, NY, 2001), Chap..
56. C. H. Papadimitriou, Computational Complexity (Addison-Wesley, Reading, MA, 1994).
57. W. Rhee, Oper. Res. Lett. ORLED5 0167-6377 10.1016/0167-6377(94)90017-5 16, 19 (1994).
58. M. Mezard and G. Parisi, J. Phys. (Paris) JOPQAG 0302-0738 47, 1285 (1986);
59. M. Mezard and G. Parisi, Europhys. Lett. EULEEJ 0295-5075 2, 913 (1986);
60. W. Krauth and M. Mezard, Europhys. Lett. EULEEJ 0295-5075 8, 213 (1989).
61. R. M. Karp, Math. Op. Res. MOREDQ 0364-765X 2, 209 (1977).
62. J. L. Jacobsen, N. Read, and H. Saleur, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.090601 90, 090601 (2003).
63. M. Mezard and G. Parisi, J. Phys. (Paris), Lett. JPSLBO 0302-072X 46, 771 (1985);
64. M. Mezard and G. Parisi, Europhys. Lett. EULEEJ 0295-5075 2, 913 (1986);
65. M. Mezard and G. Parisi, J. Phys. (Paris), Lett. JPSLBO 0302-072X 48, 1451 (1987);
66. G. Parisi and M. Ratiéville, e-print cond-mat/0204595.
67. D. A. Huse, C. L. Henley, and D. S. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.2924 55, 2924 (1985);
68. D. S. Fisher and D. A. Huse, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.43.10728 43, 10728 (1991).
69. G. Grinstein and S.-K. Ma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.2588 28, 2588 (1983);
70. D. S. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.1964 56, 1964 (1986).
71. C. Moore, e-print cond-mat/0109010.