Large-scale low-energy excitations in the two-dimensional Ising spin glass

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 9, 2002, Pages 944191-944199

  Hartmann, A K ^a,b   Young, A P ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CRYSTAL STRUCTURE; FINITE ELEMENT ANALYSIS; GLASS TRANSITION TEMPERATURE; LOW ENERGY RADIATION; MATHEMATICAL MODEL; MOLECULAR INTERACTION; MOLECULAR MODEL;

EID: 0036752835     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (52)

1. D.S. Fisher and D.A. Huse, Phys. Rev. Lett. 56, 1601 (1986).
2. D.S. Fisher and D.A. Huse, Phys. Rev. B 38, 386 (1988).
3. A. J. Bray and M. A. Moore, in Heidelberg Colloquium on Glassy Dynamics and Optimization, edited by L. Van Hemmen and I. Morgenstern (Springer, Berlin, 1986), p. 121.
4. W.L. McMillan, J. Phys. A 17, 3179 (1984).
5. A.J. Bray and M.A. Moore, J. Phys. C 17, L463 (1984).
6. W.L. McMillan, Phys. Rev. B 30, 476 (1984).
7. A.K. Hartmann, Phys. Rev. E 59, 84 (1999).
8. M. Palassini and A.P. Young, Phys. Rev. Lett. 83, 5126 (1999).
9. A.K. Hartmann, Phys. Rev. E 60, 5135 (1999).
10. K. Hukushima, Phys. Rev. E 60, 3606 (1999).
11. W.L. McMillan, Phys. Rev. B 29, 4026 (1984).
12. H. Rieger, L. Santen, U. Blasum, M. Diehl, M. Jünger, and G. Rinaldi, J. Phys. A 29, 3939 (1996).
13. M. Palassini and A.P. Young, Phys. Rev. B 60, R9919 (1999).
14. A.K. Hartmann and A.P. Young, Phys. Rev. B 64, 180404 (2001).
15. A.C. Carter, A.J. Bray, and M.A. Moore, Phys. Rev. Lett. 88, 077201 (2002).
16. A.J. Bray and M.A. Moore, Phys. Rev. Lett. 58, 57 (1987).
17. A.A. Middleton, Phys. Rev. B 63, 060202(R) (2001).
18. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979).
19. G. Parisi, J. Phys. A 13, 1101 (1980).
20. G. Parisi, Phys. Rev. Lett. 50, 1946 (1983).
21. M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
22. F. Krzakala and O.C. Martin, Phys. Rev. Lett. 85, 3013 (2000).
23. M. Palassini and A.P. Young, Phys. Rev. Lett. 85, 3017 (2000).
24. H.G. Katzgraber, M. Palassini, and A.P. Young, Phys. Rev. B 63, 184422 (2001).
25. E. Marinari and G. Parisi, Phys. Rev. B 62, 11 677 (2000).
26. M.A. Moore, cond-mat/0203469 (unpublished).
27. J. Lamarcq, J.-P. Bouchaud, O.C. Martin, and M. Mézard, cond-mat/0107544 (unpublished).
28. S. Liang, Phys. Rev. Lett. 69, 2145 (1992).
29. N. Kawashima, H. Hatano, and M. Suzuki, J. Phys. A 25, 4985 (1992).
30. N. Kawashima and M. Suzuki, J. Phys. A 25, 1055 (1992).
31. N. Kawashima and T. Aoki, J. Phys. Soc. Jpn. Suppl. A 69, 169 (2000).
32. N. Kawashima, J. Phys. Soc. Jpn. 69, 987 (2000).
33. M. Picco, F. Ritort, and M. Sales, cond-mat/0106554 (unpublished).
34. A. K. Hartmann and H. Rieger, Optimization Algorithms in Physics (Wiley-VCH, Berlin, 2001).
35. J. Houdayer, Eur. Phys. J. B 22, 479 (2001).
36. L. Bieche, J.P. Uhry, R. Maynard, and R. Rammal, J. Phys. A 13, 2553 (1980).
37. F. Barahona, J. Phys. A 15, 3241 (1982).
38. R.G. Palmer and J. Adler, Int. J. Mod. Phys. C 10, 667 (1999).
39. The "world record" seems to be L= 1800 in Ref. 38, while Ref. 14, which studied a large number of samples using readily available algorithms from the LEDA package, went up to size L = 480.
40. We are grateful to M. A. Moore for a helpful discussion on this point.
41. We should point out that there are polynomial algorithms for the d=2 Ising model with periodic boundary conditions. For example Saul and Kardar (Refs. 48, 49) (see also Ref. 50) were able to compute the partition function at finite- T in polynomial time, but this method is not as efficient as the matching algorithm and so can only do rather small sizes, and, furthermore, it does not yield the ground state spin configuration. The more efficient transfer matrix approach of Merz and Chalker (Ref. 51), based on work by Cho and Fisher (Ref. 52), also unfortunately does not give the ground state spin configuration.
42. Information about the spin glass ground state server at the University of Köln can be found at http://www.informatik.unikoeln.de/ls_juenger/projects/sgs.html
43. J. Houdayer and O.C. Martin, Europhys. Lett. 49, 794 (2000).
44. J. Houdayer, F. Krzakala, and O.C. Martin, Eur. Phys. J. B 18, 467 (2000).
45. The original definition of a sponge-like excitation (Ref. 43) required the excitation to "wrap around" in all dimensions, which is only possible for d≥3. In two dimensions, we feel it is convenient to use the same term for excitations comprising two domain walls which wrap around in one direction.
46. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1995).
47. M. Palassini, F. Liers, M. Jünger, and A. P. Young (unpublished).
48. L. Saul and M. Kardar, Phys. Rev. E 48, R3221 (1993).
49. L. Saul and M. Kardar, Nucl. Phys. B 432, 641 (1994).
50. T. Regge and R. Zecchina, J. Math. Phys. 37, 2796 (1996).
51. F. Merz and J.T. Chalker, Phys. Rev. B 65, 054425 (2002).
52. S. Cho and M.P.A. Fisher, Phys. Rev. B 55, 1025 (1997).