Fragility of the free-energy landscape of a directed polymer in random media

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

Volumn 65, Issue 6, 2002, Pages

  Sales, Marta ^a   Yoshino, Hajime ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; FREE ENERGY; MATHEMATICAL MODELS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; RANDOM PROCESSES; SPIN GLASS;

DIRECTED POLYMER IN RANDOM MEDIA (DPRM); DISORDER-AVERAGED CORRELATION FUNCTION; FREE-ENERGY LANDSCAPE; TRANSFER-MATRIX CALCULATIONS;

POLYMERS;

EID: 41349101695     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.066131     Document Type: Article

References (74)

1. A. J. Bray and M. A. Moore, Phys. Rev. Lett. 58, 57 (1987).
2. D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 386 (1988);
3. Phys. Rev. BD. S. FisherD. A. Huse38, 373 (1988).
4. D. S. Fisher and D. A. Huse, Phys. Rev. B 43, 10728 (1991).
5. J. Banavar and A. J. Bray, Phys. Rev. B 35, 8888 (1987).
6. M. Ney-Nifle and H. J. Hilhorst, Phys. Rev. Lett. 68, 2992 (1992);
7. M. Ney-NifleH. J. HilhorstPhysica A 193, 48 (1993).
8. K. Jonason, E. Vincent, J. Hamman, J. P. Bouchaud, and P. Nordblad, Phys. Rev. Lett. 81, 3243 (1998).
9. E. Vincent, J. Hammann, and M. Ocio, Recent Progress in Random Magnets (World Scientific, Singapore, 1992);P. Nordblad and P. Svedlindh, in Spin Glasses and Random Fields, edited by A. P. Young Series on Directions in Condensed Matter Physics Vol. 12 (World Scientific, Singapore, 1998).
10. P. E. Jönsson, H. Yoshino, and P. Nordblad, e-print cond-mat/0203444.
11. F. Ritort, Phys. Rev. B 50, 6844 (1994).
12. V. Azcoiti, E. Follana, and F. Ritort, J. Phys. A 28, 3863 (1995).
13. H. Rieger, L. Santen, U. Blasum, M. Diehl, and M. Jünger, J. Phys. A 29, 3939 (1996).
14. M. Ney-Nifle, Phys. Rev. B 57, 492 (1997).
15. Sompolinski (unpublished) cited in p. 886 of K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).
16. I. Kondor, J. Phys. A 22, L163 (1989).
17. I. Kondor and A. Végsö, J. Phys. A 26, L641 (1993).
18. S. Franz and M. Ney-Nifle, J. Phys. A 28, 2499 (1995).
19. T. Rizzo, J. Phys. A 34, 5531 (2001).
20. D. A. Huse and L-F. Ko, Phys. Rev. B 56, 14597 (1997).
21. A. Billoire and E. Marinari, J. Phys. A 33, L265 (2000).
22. R. Mulet, A. Pagnani, and G. Parisi, Phys. Rev. B 63, 184438 (2001).
23. A. Billoire and E. Marinari, e-print cond-mat/0202473.
24. M. Sales and H. Yoshino, e-print cond-mat/0112384.
25. For a review of directed polymer in random media, see T. Halpin-Healy and Y. C. Zhang, Phys. Rep. 254, 215 (1995).
26. M. Mézard, J. Phys. I 51, 1831 (1990).
27. Y. C. Zhang, Phys. Rev. Lett. 59, 2125 (1987).
28. M. V. Feigel’man and V. M. Vinokur, Phys. Rev. Lett. 61, 1139 (1988).
29. Y. Shapir, Phys. Rev. Lett. 66, 1473 (1991).
30. T. Halpin-Healy and D. Herbert, Phys. Rev. E 48, R1617 (1993).
31. M. Mézard and G. Parisi, J. Phys. I 1, 809 (1991).
32. L. Balents and D. S. Fisher, Phys. Rev. B 48, 5949 (1993).
33. L. Balents, J. P. Bouchaud, and M. Mézard, J. Phys. I 6, 1007 (1996).
34. T. Giamarichi and P. Le. Doussal, Phys. Rev. Lett. 72, 1530 (1994);
35. T. GiamarichiP. Le. DoussalPhys. Rev. B 52, 1242 (1995).
36. P. Chauve, T. Giamarchi, and P. Le Doussal, Phys. Rev. B 62, 6241 (2000).
37. D. A. Huse and C. L. Henley, Phys. Rev. Lett. 54, 2708 (1985).
38. S. Lemerle, J. Ferré, C. Chappert, V. Mathet, T. Giamarchi, and P. Le Doussal, Phys. Rev. Lett. 80, 849 (1998).
39. G. Blatter, M. V. Feigel’man, V. B. Genkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).
40. C. A. Bolle, Nature (London) 399, 43 (1999).
41. H. Fukuyama and P. A. Lee, Phys. Rev. B 17, 535 (1978).
42. G. Grüner, Rev. Mod. Phys. 66, 1129 (1988).
43. G. Parisi and M. A. Virasoro, J. Phys. (France) 50, 3317 (1989).
44. M. Kardar, Nucl. Phys. B 290, 582 (1987).
45. M. Kardar, in Proceedings of Fluctuating Geometries in Statistical Mechanics and Field Theory, edited by F. Daivid, P. Ginzparg, and J. Zinn-Justin (Elsevier, Amsterdam 1996).
46. D. A. Gorokhov and G. Blatter, Phys. Rev. Lett. 82, 2705 (1999).
47. G. Parisi, J. Phys. A 13, L115 (1980);
48. J. Phys. AG. Parisi13, 1101 (1980);
49. J. Phys. AG. Parisi13, 1887 (1980).
50. M. Mézard, G. Parisi, and M. A. Virasoro, Spin-Glass Theory and Beyond (World Scientific, Singapore, 1988).
51. G. Parisi, J. Phys. I 51, 1595 (1990).
52. A. I. Larkin, Sov. Phys. JETP 31, 784 (1970).
53. In the spin-glass problems the chaos exponent is denoted as (Formula presented). Here we do not use the convention because it is usually used for the roughness exponent (Formula presented).
54. We observed the following numerically within the lattice model we used in Sec. VII D. We computed root-mean-square average of the sample-to-sample fluctuations of energy, entropy, and free energy. Fluctuation of energy with respect to the mean value depends on temperature T as (Formula presented), where c is a numerical constant. Note that the (Formula presented) behavior shows up only at sufficiently large length scales (as found in 3). The temperature dependence is consistent with the observation that fluctuation of energy at (Formula presented) (ground state) scales as (Formula presented), which is often assumed in the scaling arguments. On the other hand the entropic fluctuation scales as (Formula presented), which is consistent with the observation that the fluctuation of free energy (Formula presented) scales as (Formula presented).
55. G. Forgacs, R. Lipowsky, and Th. M. Nieuwenhuizen, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, Kondon, 1991), Vol 14.
56. T. Hwa and D. S. Fisher, Phys. Rev. B 49, 3136 (1994).
57. U. Shulz, J. Villain, E. Brézin, and H. Orland, J. Stat. Phys. 51, 1 (1988).
58. J. P. Bouchaud and H. Orland, J. Stat. Phys. 61, 877 (1990).
59. D. A. Huse, C. L. Henley, and D. S. Fisher, Phys. Rev. Lett. 55, 2924 (1985).
60. To treat the replica number n as a scaling variable has been proposed by several authors 2342.
61. The choice of renormalized D in Eq. (82) allowed to simplify the calculation. One can work also with the original D and will find the same positive (Formula presented) of order (Formula presented) up to some irrelevant differences.
62. Ya. G. Sinai, Theor. Probab. Appl. 27, 247 (1982).
63. M. Kardar, Phys. Rev. Lett. 55, 2923 (1985).
64. Note that here we do not use rescaled variables such as in Eq. (98).
65. The same results are obtained if we consider that the two strings are tilted with (Formula presented) and (Formula presented), respectively.
66. M. Mézard and G. Parisi, J. Phys. A 25, 4521 (1992).
67. K. Jonasson, J. Mattson, and P. Nordblad, Phys. Rev. Lett. 77, 2562 (1996);
68. K. Jonason and P. Nordblad, Eur. Phys. J. B 10, 23 (1999).
69. E. Vincent, F. Alet, J. Hammann, M. Ocio, and J. P. Bouchaud, Europhys. Lett. 50, 674 (2000).
70. H. Yoshino, A. Lemaitre, and J. P. Bouchaud, Eur. Phys. J. B 20, 367 (2000).
71. J-P. Bouchaud, in Soft and Fragile Matter, edited by M. E. Cates and M. R. Evans (Institute of Physics, Bristol, 2000);e-print cond-mat/9910387.
72. J. P. Bouchaud, V. Dupuis, J. Hammann, and E. Vincent, Phys. Rev. B 65, 024439 (2001).
73. L. Bertheir and J.-P. Bouchaud, e-print cond-mat/0202069.
74. H. Yoshino, Phys. Rev. Lett. 81, 1493 (1998); and(unpublished).