Specific-heat exponent of random-field systems via ground-state calculations

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 21, 2001, Pages

  Hartmann, A K ^a   Young, A P ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

ALGORITHM; ARTICLE; MAGNETIC FIELD; MAGNETISM; MATHEMATICAL ANALYSIS; MOLECULAR MODEL; STATISTICAL ANALYSIS; SYSTEM ANALYSIS; TEMPERATURE DEPENDENCE;

EID: 0035581595     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.214419     Document Type: Article

References (50)

1. Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975).
2. D. P. Belanger and A. P. Young, J. Magn. Magn. Mater. 100, 272 (1991).
3. H. Rieger, in Annual Reviews of Computational Physics II, edited by D. Stauffer (World Scientific, Singapore, 1995), pp. 295–341.
4. See, e.g., the articles by D. P. Belanger and T. Nattermann in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998).
5. S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979).
6. A. J. Bray and M. A. Moore, J. Phys. C 18, L927 (1985).
7. D. S. Fisher, Phys. Rev. Lett. 56, 416 (1985).
8. J. C. Anglès d’Auriac, M. Preissmann, and A. Seb, J. Math. Comp. Model. 26, 1 (1997).
9. H. Rieger, in Advances in Computer Simulation, edited by J. Kertesz and I. Kondor, Lecture Notes in Physics Vol. 501 (Springer, Heidelberg, 1998).
10. M. J. Alava, P. M. Duxbury, C. Moukarzel, and H. Rieger, in Phase Transitions and Critical Phenomena, Vol. 18, edited by C. Domb and J. L. Lebowitz, (Academic, New York, 2001).
11. A. K. Hartmann and H. Rieger, Optimization Algorithms in Physics (Wiley-VCH, Berlin, in press).
12. A. A. Middleton and D. S. Fisher (unpublished).
13. H. Rieger, Phys. Rev. B 52, 6659 (1995)
14. see also H. Rieger and A. P. Young, J. Phys. A 26, 5279 (1993).
15. D. P. Belanger, A. R. King, V. Jaccarino, and J. L. Cardy, Phys. Rev. B 28, 2522 (1983)
16. D. P. Belanger and Z. Slanič, J. Magn. Magn. Mater. 186, 65 (1998).
17. M. N. S. Swamy and K. Thulasiraman, Graphs, Networks and Algorithms (Wiley, New York, 1991).
18. J. D. Claiborne, Mathematical Preliminaries for Computer Networking (Wiley, New York, 1990).
19. W. Knödel, Graphentheoretische Methoden und ihre Anwendung (Springer, Berlin, 1969).
20. K. Mehlhorn and St. Näher, The LEDA Platform of Combinatorial and Geometric Computing (Cambridge University Press, Cambridge, 1999);see also http://www.mpi-sb.mpg.de/LEDA/leda.html
21. J.-C. Picard and H. D. Ratliff, Network 5, 357 (1975).
22. J. L. Träff, Eur. J. Oper. Res. 89, 564 (1996).
23. R. E. Tarjan, Data Structures and Network Algorithms (Society for Industrial and Applied Mathematics, Philadelphia, 1983).
24. A. V. Goldberg and R. E. Tarjan, J. ACM 35, 921 (1988).
25. B. Cherkassky and A. Goldberg, Algorithmica 19, 390 (1997).
26. A.V. Goldberg, R. Satish, J. ACM 45, 783 (1998).
27. A. T. Ogielski, Phys. Rev. Lett. 57, 1251 (1986).
28. A. K. Hartmann and U. Nowak, Eur. Phys. J. B 7, 105 (1999).
29. J.-C. Anglès d’Auriac and N. Sourlas, Europhys. Lett. 39, 473 (1997).
30. N. Sourlas, Comput. Phys. Commun. 121-122, 183 (1999).
31. U. Nowak, K.D. Usadel, and J. Esser, Physica A 250, 1 (1998).
32. The RFIM with a delta-distribution of the random fields (Formula presented) exhibits an exponential ground-state degeneracy.
33. J.-C. Picard and M. Queyranne, Math. Prog. Study 13, 8 (1980).
34. A. K. Hartmann, Physica A 248, 1 (1998).
35. S. Bastea and P.M. Duxbury, Phys. Rev. E 58, 4261 (1998).
36. Actually we used more samples for some values of h than for others. Hence, for each data point, we only used realizations where the ground states were calculated at both the left and the right boundary of the corresponding interval.
37. B. Efron, The Jackknife, The Bootstrap and Other Resampling Plans (SIAM, Philadelphia, 1982).
38. W. H. Press, S.A. Teukolsky, W. T. Vetterling, and B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1995).
39. We used the Levenberg-Marquardt routine described in Ref. 36.
40. G. Grinstein, Phys. Rev. Lett. 37, 944 (1976).
41. J. Villain, J. Phys. (France) 46, 1843 (1985).
42. M. Gofman, J. Adler, A. Aharony, A. B. Harris, and M. Schwartz, Phys. Rev. Lett. 71, 1569 (1993).
43. M. Schwartz and A. Soffer, Phys. Rev. Lett. 55, 2499 (1985).
44. A. Aharony, Phys. Rev. B 18, 3318 (1978).
45. A. Houghton, A. Khurana, and F. J. Seco, Phys. Rev. B 34, 1700 (1986)
46. A. Houghton, A. Khurana, and F. J. Seco, Phys. Rev. Lett. 55, 856 (1985).
47. V. Privman, P. C. Hohenberg, and A. Aharony, in Phase Transitions and Critical Phenomena, Vol. 14, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1991), p. 1.
48. See, for example, the discussion on p. 11 of Ref. 44.
49. C. Bervillier, Phys. Rev. B 34, 8141 (1986).
50. A. A. Middleton and D. S. Fisher, cond-mat/0107489 (unpublished).