Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 1 A, 2000, Pages 103-112

  Bray, A J ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS;

LANGEVIN EQUATIONS; NONEQUILIBRIUM CRITICAL DYNAMICS; PERSISTENCE PHENOMENA; POWER-LAW POTENTIAL;

MOLECULAR DYNAMICS;

EID: 0034225497     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.103     Document Type: Article

References (42)

1. For a recent review see S.N. Majumdar, Curr. Sci. India 77, 370 (1999).
2. B. Derrida, A.J. Bray, and C. Godrèche, J. Phys. A 27, L357 (1994); B. Derrida, V. Hakim, and V. Pasquier, Phys. Rev. Lett. 75, 751 (1995); J. Stat. Phys. 85, 763 (1996).
3. B. Derrida, A.J. Bray, and C. Godrèche, J. Phys. A 27, L357 (1994); B. Derrida, V. Hakim, and V. Pasquier, Phys. Rev. Lett. 75, 751 (1995); J. Stat. Phys. 85, 763 (1996).
4. B. Derrida, A.J. Bray, and C. Godrèche, J. Phys. A 27, L357 (1994); B. Derrida, V. Hakim, and V. Pasquier, Phys. Rev. Lett. 75, 751 (1995); J. Stat. Phys. 85, 763 (1996).
5. D. Stauffer, J. Phys. A 27, 5029 (1994).
6. S.N. Majumdar, C. Sire, A.J. Bray, and S.J. Cornell, Phys. Rev. Lett. 77, 2867 (1996); B. Derrida, V. Hakim, and R. Zeitak, ibid. 77, 2871 (1996).
7. S.N. Majumdar, C. Sire, A.J. Bray, and S.J. Cornell, Phys. Rev. Lett. 77, 2867 (1996); B. Derrida, V. Hakim, and R. Zeitak, ibid. 77, 2871 (1996).
8. J. Krug, H. Kallahis, S.N. Majumdar, S.J. Cornell, A.J. Bray, and C. Sire, Phys. Rev. E 56, 2702 (1997).
9. A.J. Bray, B. Derrida, and C. Godrèche, Europhys. Lett. 27, 175 (1994); P.L. Krapivsky, E. Ben-Naim, and S. Redner, Phys. Rev. E 50, 2474 (1994); S.N. Majumdar and C. Sire, Phys. Rev. Lett. 77, 1420 (1996).
10. A.J. Bray, B. Derrida, and C. Godrèche, Europhys. Lett. 27, 175 (1994); P.L. Krapivsky, E. Ben-Naim, and S. Redner, Phys. Rev. E 50, 2474 (1994); S.N. Majumdar and C. Sire, Phys. Rev. Lett. 77, 1420 (1996).
11. A.J. Bray, B. Derrida, and C. Godrèche, Europhys. Lett. 27, 175 (1994); P.L. Krapivsky, E. Ben-Naim, and S. Redner, Phys. Rev. E 50, 2474 (1994); S.N. Majumdar and C. Sire, Phys. Rev. Lett. 77, 1420 (1996).
12. J. Cardy, J. Phys. A 28, L19 (1995); E. Ben-Naim, Phys. Rev. E 53, 1566 (1996); M. Howard, J. Phys. A 29, 3437 (1996); S.J. Cornell and A.J. Bray, Phys. Rev. E 54, 1153 (1996).
13. J. Cardy, J. Phys. A 28, L19 (1995); E. Ben-Naim, Phys. Rev. E 53, 1566 (1996); M. Howard, J. Phys. A 29, 3437 (1996); S.J. Cornell and A.J. Bray, Phys. Rev. E 54, 1153 (1996).
14. J. Cardy, J. Phys. A 28, L19 (1995); E. Ben-Naim, Phys. Rev. E 53, 1566 (1996); M. Howard, J. Phys. A 29, 3437 (1996); S.J. Cornell and A.J. Bray, Phys. Rev. E 54, 1153 (1996).
15. J. Cardy, J. Phys. A 28, L19 (1995); E. Ben-Naim, Phys. Rev. E 53, 1566 (1996); M. Howard, J. Phys. A 29, 3437 (1996); S.J. Cornell and A.J. Bray, Phys. Rev. E 54, 1153 (1996).
16. M. Marcos-Martin, D. Beysens, J-P. Bouchaud, C. Godrèche, and I. Yekutieli, Physica D 214D, 396 (1995).
17. W.Y. Tam, R. Zeitak, K.Y. Szeto, and J. Stavans, Phys. Rev. Lett. 78, 1588 (1997).
18. B. Yurke, A.N. Pargellis, S.N. Majumdar, and C. Sire, Phys. Rev. E 56, R40 (1997).
19. S.N. Majumdar, A.J. Bray, S.J. Cornell, and C. Sire, Phys. Rev. Lett. 77, 3704 (1996); K. Oerding, S.J. Cornell, and A.J. Bray, Phys. Rev. E 56, R25 (1997).
20. S.N. Majumdar, A.J. Bray, S.J. Cornell, and C. Sire, Phys. Rev. Lett. 77, 3704 (1996); K. Oerding, S.J. Cornell, and A.J. Bray, Phys. Rev. E 56, R25 (1997).
21. H.K. Janssen, B. Schaub, and B. Schmittmann, Z. Phys. B: Condens. Matter 73, 539 (1989).
22. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973); J.M. Kosterlitz, ibid. 7, 1046 (1974); P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987).
23. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973); J.M. Kosterlitz, ibid. 7, 1046 (1974); P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987).
24. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973); J.M. Kosterlitz, ibid. 7, 1046 (1974); P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987).
25. Similar results have been obtained independently, in a different context, by J-P. Bouchaud (private communication), and in earlier work on tracer dispersion in planar multipole flows by J. Koplik, S. Redner, and E.J. Hinch, Phys. Rev. E 50, 4650 (1994); Phys. Rev. Lett. 74, 82 (1995).
26. Similar results have been obtained independently, in a different context, by J-P. Bouchaud (private communication), and in earlier work on tracer dispersion in planar multipole flows by J. Koplik, S. Redner, and E.J. Hinch, Phys. Rev. E 50, 4650 (1994); Phys. Rev. Lett. 74, 82 (1995).
27. Similar results have been obtained independently, in a different context, by J-P. Bouchaud (private communication), and in earlier work on tracer dispersion in planar multipole flows by J. Koplik, S. Redner, and E.J. Hinch, Phys. Rev. E 50, 4650 (1994); Phys. Rev. Lett. 74, 82 (1995).
28. A.J. Bray and A.J. McKane, Phys. Rev. Lett. 62, 493 (1989).
29. T.J. Newman, A.J. Bray, and A.J. McKane, Phys. Rev. A 41, 657 (1990).
30. A.J. Bray, A.J. Briant, and D.K. Jervis, Phys. Rev. Lett. 84, 1503 (2000).
31. P.C. Hohenberg and B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977).
32. A.D. Rutenberg and A.J. Bray, Phys. Rev. E 51, R1641 (1995).
33. B. Yurke, A.N. Pargellis, T. Kovacs, and D.A. Huse, Phys. Rev. E 47, 1525 (1993), and references therein; G. Ryskin and M. Kremenetsky, Phys. Rev. Lett. 67, 1574 (1991).
34. B. Yurke, A.N. Pargellis, T. Kovacs, and D.A. Huse, Phys. Rev. E 47, 1525 (1993), and references therein; G. Ryskin and M. Kremenetsky, Phys. Rev. Lett. 67, 1574 (1991).
35. A.D. Rutenberg and A.J. Bray, Phys. Rev. E 51, 5499 (1995).
36. D. A. Huse (private communication).
37. R.E. Blundell, K. Humayun, and A.J. Bray, J. Phys. A 25, L733 (1992).
38. Z.B. Li, L. Schülke, and B. Zheng, Phys. Rev. Lett. 74, 3396 (1995).
39. R. Gupta and C.F. Baillie, Phys. Rev. B 45, 2883 (1992).
40. H.J. Luo, M. Schulz, L. Schülke, S. Trimper, and B. Zheng, Phys. Lett. A 250, 383 (1998).
41. A. Linke, D.W. Heerman, P. Altevogt, and M. Siegert, Physica A 222, 205 (1995) obtained z = 2.160(5) from the relaxation of the magnetization from an initially ordered state, while z = 2.14(1) was obtained in Ref. [18] using finite-size scaling of the time-dependent Binder parameter with disordered initial conditions. Both of these fall in the range 2.13-2.17 obtained by a number of other authors, e.g; S. Tang and D.P. Landau, Phys. Rev. B 36, 567 (1987).
42. A. Linke, D.W. Heerman, P. Altevogt, and M. Siegert, Physica A 222, 205 (1995) obtained z = 2.160(5) from the relaxation of the magnetization from an initially ordered state, while z = 2.14(1) was obtained in Ref. [18] using finite-size scaling of the time-dependent Binder parameter with disordered initial conditions. Both of these fall in the range 2.13-2.17 obtained by a number of other authors, e.g; S. Tang and D.P. Landau, Phys. Rev. B 36, 567 (1987).