Ground-state and domain-wall energies in the spin-glass region of the two-dimensional ±j random-bond Ising model

Physical Review B - Condensed Matter and Materials Physics

Volumn 75, Issue 17, 2007, Pages

  Fisch, Ronald ^a   Hartmann, Alexander K ^b  

^a Universität Göttingen ^*  (United States)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34347231285     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.75.174415     Document Type: Article

References (45)

1. S. F. Edwards and P. W. Anderson, J. Phys. F: Met. Phys. JPFMAT 0305-4608 10.1088/0305-4608/5/5/017 5, 965 (1975).
2. Reviews on spin glasses can be found in K. Binder and A. P. Young, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.58.801 58, 801 (1986);
3. M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987);
4. K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, 1991);
5. Spin Glasses and Random Fields, edited by, A. P. Young, (World Scientific, Singapore, 1998).
6. A. J. Bray and M. A. Moore, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.631 31, 631 (1985).
7. D. S. Fisher and D. A. Huse, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.1601 56, 1601 (1986).
8. C. Amoruso, E. Marinari, O. C. Martin, and A. Pagnani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.087201 91, 087201 (2003).
9. A. K. Hartmann and M. A. Moore, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.127201 90, 127201 (2003).
10. A. J. Bray and M. A. Moore, Heidelberg Colloquium on Glassy Dynamics, edited by, J. L. van Hemmen, and, I. Morgenstern, (Springer, Berlin, 1986), pp. 121-153.
11. A. K. Hartmann and A. P. Young, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.180404 64, 180404 (R) (2001).
12. C. Wang, J. Harrington, and J. Preskill, Ann. Phys. (N.Y.) APNYA6 0003-4916 303, 31 (2003).
13. T. Jörg, J. Lukic, E. Marinari, and O. C. Martin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.237205 96, 237205 (2006).
14. R. Fisch, arXiv:cond-mat/0607622, J. Stat. Phys. (to be published).
15. Y. Ozeki and H. Nishimori, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/26/14/009 26, 3399 (1993).
16. S. Kirkpatrick, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.16.4630 16, 4630 (1977).
17. C. Amoruso and A. K. Hartmann, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.134425 70, 134425 (2004).
18. W. L. McMillan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.29.4026 29, 4026 (1984).
19. F. Merz and J. T. Chalker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.054425 65, 054425 (2002).
20. J.-S. Wang and R. H. Swendsen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.4840 38, 4840 (1988).
21. L. Saul and M. Kardar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48. R3221 48, R3221 (1993).
22. L. Saul and M. Kardar, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90037-X 432, 641 (1994).
23. J. Lukic, A. Galluccio, E. Marinari, O. C. Martin, and G. Rinaldi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.117202 92, 117202 (2004).
24. D. S. Fisher and D. A. Huse, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.386 38, 386 (1988).
25. R. Fisch, J. Stat. Phys. JSTPBS 0022-4715 125, 793 (2006).
26. A. E. Ferdinand and M. E. Fisher, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.185.832 185, 832 (1969).
27. H. Park and M. den Nijs, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.565 38, 565 (1988).
28. A. C. Carter, A. J. Bray, and M. A. Moore, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.077201 88, 077201 (2002).
29. A. K. Hartmann, A. J. Bray, A. C. Carter, M. A. Moore, and A. P. Young, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.224401 66, 224401 (2002).
30. A. K. Hartmann and H. Rieger, Optimization Algorithms in Physics (Wiley-VCH, Berlin, 2001).
31. A. K. Hartmann and H. Rieger, New Optimization Algorithms in Physics (Wiley-VCH, Berlin, 2004).
32. I. Bieche, R. Maynard, R. Rammal, and J. P. Uhry, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/13/8/005 13, 2553 (1980).
33. F. Barahona, R. Maynard, R. Rammal, and J. P. Uhry, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/15/2/033 15, 673 (1982).
34. U. Derigs and A. Metz, Math. Program. MHPGA4 0025-5610 10.1007/BF01594929 50, 113 (1991).
35. W. J. Cook, W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver, Combinatorial Optimization (Wiley, New York, 1998).
36. B. Korte and J. Vygen, Combinatorial Optimization-Theory and Algorithms (Springer, Heidelberg, 2000).
37. K. Mehlhorn and St. Näher, The LEDA Platform of Combinatorial and Geometric Computing (Cambridge University Press, Cambridge, 1999);
38. see also http://www.algorithmic-solutions.de
39. I. A. Campbell, A. K. Hartmann, and H. G. Katzgraber, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.054429 70, 054429 (2004).
40. J.-P. Bouchaud, F. Krzakala, and O. C. Martin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.224404 68, 224404 (2003).
41. J. Wehr and M. Aizenman, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01314921 60, 287 (1990).
42. M. N. Barber, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, J. L. Lebowitz, (Academic, London, 1983), Vol. 8, pp. 145-266.
43. We used the nonlinear least-squares Marquardt-Levenberg algorithm of the GNUPLOT program, see http://www.gnuplot.info/
44. A. K. Hartmann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.056102 65, 056102 (2002).
45. H. G. Katzgraber, M. Körner, F. Liers, M. Jünger, and A. K. Hartmann, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.094421 72, 094421 (2005).