Exact results and open questions in first principle functional RG

Annals of Physics

Volumn 325, Issue 1, 2010, Pages 49-150

  Le Doussal, Pierre ^a  

^a LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

Burgers equation; Disordered systems; Glasses; Pinning; Renormalization group; Turbulence

Indexed keywords

EID: 73449148996     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2009.10.010     Document Type: Article

References (119)

1. Zinn-Justin J. Quantum Field Theory and Critical Phenomena (1989), Oxford University Press, Oxford
2. Carpentier D., and Le Doussal P. Nucl. Phys. B 588 (2000) 565 cond-mat/9908335
3. Carpentier D., and Le Doussal P. Phys. Rev. Lett. 81 (1998) 2558 cond-mat/9802083 (and references cited therein)
4. Carpentier D., and Le Doussal P. Phys. Rev. E 63 (2001) 026110 cond-mat/0003281
5. Le Doussal P., and Giamarchi T. Physica C 331 (2000) 233 cond-mat/9810218
6. Castillo H.E., Chamon C., Fradkin E., Goldbart P.M., and Mudry C. Phys. Rev. B 56 (1997) 10668
7. Horovitz B., and Le Doussal P. Phys. Rev. B 65 (2002) 125323 cond-mat/0108143
8. Mudry C., Ryu S., and Furusaki A. Phys. Rev. B 67 (2003) 064202 cond-mat/0207723
9. Fisher D.S. Phys. Rev. B 50 (1994) 3799
10. Fisher D.S. Phys. Rev. B 51 (1995) 6411
11. Le Doussal P., Monthus C., and Fisher D.S. Phys. Rev. E 59 (1999) 4795 cond-mat/9811300
12. Fisher D.S., Le Doussal P., and Monthus C. Phys. Rev. E 64 (2001) 066107 cond-mat/0012290
13. Fisher D.S., Le Doussal P., and Monthus C. Phys. Rev. Lett. 80 (1998) 3539 cond-mat/9710270
14. F. Igloi, C. Monthus, Phys. Rep. 412 (2005) 277.
15. Blatter G., Feigel'man M.V., Geshkenbein V.B., Larkin A.I., and Vinokur V.M. Rev. Mod. Phys. 66 (1994) 1125
16. T. Giamarchi, P. Le Doussal, Phys. Rev. B 52 (1995) 1242, cond-mat/9705096, in: A.P. Young (Ed.), Spin Glasses and Random Fields, World Scientific, Singapore, 1997.
17. Nattermann T., and Scheidl S. Adv. Phys. 49 (2000) 607-704
18. Rosso A., and Krauth W. Phys. Rev. Lett. 87 (2001) 187002
19. Rosso A., and Krauth W. Phys. Rev. B 65 (2001) 012202
20. Rosso A., Hartmann A., and Krauth W. Phys. Rev. E 67 (2003) 021602
21. Roters L., Lubeck S., and Usadel K.D. Phys. Rev. E 66 (2002) 026127
22. Roters L., Lubeck S., and Usadel K.D. Phys. Rev. E 66 (2002) 069901E
23. P. Le Doussal, Euro-Summer School on Condensed Matter Theory 2004, lecture notes at http://www.lancs.ac.uk/users/esqn/windsor04/program.htm.
24. P. Le Doussal, Beg Rohu School of Physics 2008, lecture notes at http://ipht.cea.fr/Meetings/BegRohu2008/notes.html.
25. Kay Joerg Wiese, in: Proceedings of STATPHYS 22, Pramana 64 (2005) 817-827 cond-mat/0511529.
26. Wiese K.J., and Le Doussal P. Markov Process. Relat. Fields 13 (2007) 777-818 cond-mat/0611346
27. Huse D.A., Henley C.L., and Fisher D.S. Phys. Rev. Lett. 56 (1986) 899
28. Kardar M. Nucl. Phys. B 290 (1987) 582
29. Balents L., and Kardar M. Phys. Rev. B 49 (1994) 13030
30. T. Emig, M. Kardar, cond-mat/0101247.
31. Imbrie J.Z., and Spencer T. J. Stat. Phys. 52 (1988) 609
32. Brunet E., and Derrida B. Phys. Rev. E 61 (2000) 6789-6801 cond-mat/0005352
33. Brunet E., and Derrida B. Physica A 279 (2000) 398-407 cond-mat/0005355
34. Johansson K. Commun. Math. Phys. 209 (2000) 437-476 math.PR/9910146, math.CO/9903134
35. Baik J., Deift P., and Johansson K. J. Am. Math. Soc. 12 4 (1999) 1119-1178 math.CO/9810105
36. Schulz U., Villain J., Brezin E., and Orland H. J. Stat. Phys. 51 (1988) 1-27
37. Hwa T., and Fisher D.S. Phys. Rev. B 49 (1994) 3136-3154
38. Le Doussal P., and Monthus C. Physica A 317 (2003) 140 cond-mat/0204168
39. McMillan W.L. J. Phys. C 17 (1984) 3179
40. Bray A.J., and Moore M.A. J. Phys. C 17 (1984) L463
41. Bray A.J., and Moore M.A. In: van Hemmen, and Morgenstern I. (Eds). Heilderberg Colloquium on Glassy Dynamics and Optimization (1986), Springer, Heidelberg
42. Fisher D.S., and Huse D.A. Phys. Rev. B 38 (1988) 373-386
43. Fisher D.S., and Huse D.A. Phys. Rev. B 43 (1991) 10728
44. Mézard M., and Parisi G. J. Phys. I (France) 1 (1991) 809
45. See, e.g. Middleton A.A. Phys. Rev. B 63 (2001) 60202
46. Hwa T., and Fisher D.S. Phys. Rev. B 49 (1994) 3136
47. Balents L., and Le Doussal P. Europhys. Lett. 65 (2004) 685
48. Balents L., and Le Doussal P. Phys. Rev. E 69 (2004) 061107 cond-mat/0312338
49. Balents L., and Le Doussal P. Ann. Phys. 315 (2005) 213 cond-mat/0408048
50. Larkin A.I., and Ovchinnikov Y.N. J. Low Temp. Phys. 34 (1979) 409
51. Efetov K.B., and Larkin A.I. Sov. Phys. JETP 45 (1977) 1236
52. Aharony A., Imry Y., and Ma S.K. Phys. Rev. Lett. 37 (1976) 1364-1367
53. Grinstein G. Phys. Rev. Lett. 37 (1976) 944-947
54. N where N is the number of unstable directions (see e.g. [44]). Hence, it cannot select low energy states.
55. Parisi G., and Sourlas N. Phys. Rev. Lett. 46 (1981) 871
56. Parisi G., and Sourlas N. Phys. Rev. Lett. 43 (1979) 744
57. Cardy J.L. Phys. Lett. 125 (1983) 470
58. See e.g. J. Kurchan, cond-mat/0209399.
59. Fisher D.S. Phys. Rev. Lett. 56 (1986) 1964
60. Balents L., and Fisher D.S. Phys. Rev. B 48 (1993) 5959
61. Balents L., Bouchaud J.P., and Mézard M. J. Phys. I 6 (1996) 1007-1020
62. Nattermann T., Stepanow S., Tang L.H., and Leschhorn H. J. Phys. II Fr. 2 (1992) 1483-1488
63. Narayan O., and Fisher D.S. Phys. Rev. B 48 (1993) 7030-7042
64. Balents L. Europhys. Lett. 24 (1993) 489
65. Giamarchi T., Le Doussal P., and Orignac E. Phys. Rev. B 64 (2001) 245119 cond-mat/0104583
66. Chauve P., Le Doussal P., and Giamarchi T. Phys. Rev. B 61 (2000) R11906 cond-mat/9910197
67. Chauve P., Le Doussal P., and Wiese K.J. Phys. Rev. Lett. 86 (2001) 1785 cond-mat/0006056
68. Chauve P., and Le Doussal P. Phys. Rev. E 64 (2001) 051102
69. S. Scheidl, Y. Dincer, 2000, cond-mat/0006048.
70. Le Doussal P., Wiese K.J., and Chauve P. Phys. Rev. E 69 (2004) 026112 cond-mat/0304614
71. Le Doussal P., Wiese K.J., and Chauve P. Phys. Rev. B 66 (2002) 174201
72. P. Le Doussal, K.J. Wiese, in preparation.
73. Le Doussal P., and Wiese K.J. Phys. Rev. E 72 (2005) 035101 cond-mat/0501315
74. Le Doussal P., and Wiese K.J. Phys. Rev. Lett. 96 (2006) 197202 cond-mat/0510344
75. Le Doussal P., and Wiese K.J. Phys. Rev. Lett. 98 (2007) 269704
76. Feldman D.E. Phys. Rev. Lett. 88 (2002) 177202
77. Tarjus G., and Tissier M. Phys. Rev. Lett. 93 (2004) 267008
78. Tarjus G., and Tissier M. Phys. Rev. Lett. 96 (2006) 087202
79. Tarjus G., and Tissier M. Phys. Rev. B 74 (2006) 214419
80. Middleton A.A. Phys. Rev. Lett. 68 (1992) 670
81. For a complete proof of Middleton's theorem, cf. Baesens C., and MacKay R.S. Nonlinearity 11 (1998) 949
82. P. Le Doussal, K.J. Wiese, cond-mat/0109204.
83. Le Doussal P., and Wiese K.J. Phys. Rev. Lett. 89 (2002) 125702 cond-mat/0305634
84. Le Doussal P., and Wiese K.J. Phys. Rev. B 68 (2003) 174202 cond-mat/0406297
85. Le Doussal P., Muller M.M., and Wiese K.J. Phys. Rev. B 77 (2008) 064203
86. Chauve P., Giamarchi T., and Le Doussal P. Europhys. Lett. 44 (1998) 110 cond-mat/9804190
87. Chauve P., Giamarchi T., and Le Doussal P. Phys. Rev. B 62 (2000) 6241 cond-mat/0002299
88. Schehr G., and Le Doussal P. Phys. Rev. E 68 (2003) 046101
89. L. Balents, P. Le Doussal, unpublished.
90. Le Doussal P. Europhys. Lett. 76 (2006) 457
91. Middleton A.A., Le Doussal P., and Wiese K.J. Phys. Rev. Lett. 98 (2007) 155701 cond-mat/0606160
92. Le Doussal P., and Wiese K.J. EPL 77 (2007) 66001 cond-mat/0610525
93. P. Le Doussal, K.J. Wiese, 0808.3217.
94. Rosso A., Le Doussal P., and Wiese K.J. Phys. Rev. B 75 (2007) 220201 cond-mat/0610821
95. P. Le Doussal, A. Middleton, K. Wiese, 0803.1142; P. Le Doussal, K. Wiese, Phys. Rev. E 79 (2009) 051106.
96. For review, see e.g. D. Bernard, cond-mat/0007106.
97. U. Frisch, J. Bec, nlin.CD/0012033, in: M. Lesieur, A. Yaglom, F. David (Eds.), New Trends in Turbulence, Springer EDP-Sciences, 2001, pp. 341-383.
98. For review, see J. Bec, K. Khanin, 2007, 0704.1611.
99. J.P. Bouchaud, M. Mezard, G. Parisi, cond-mat/9503144.
100. D. Bernard, K. Gawedzki, chao-dyn/9805002.
101. Bauer M., and Bernard D. J. Phys. A 3 (1999) 5179-5199 chao-dyn/9812018
102. Burgers J.M. The Nonlinear Diffusion Equation (1974), Reidel, Dordrecht
103. L. Frachebourg, Ph.A. Martin, cond-mat/9905056.
104. L. Frachebourg, Ph.A. Martin, J. Piasecki, cond-mat/9911346.
105. A.M. Polyakov, hep-th/9506189.
106. a]. This gauge choice is fixed by the sample dependent definition of over(V, ^) chosen here.
107. Le Doussal P. Phys. Rev. Lett. 96 (2006) 235702 cond-mat/0505679
108. See e.g. [65] for review.
109. (n) (0, ..., 0)). They are also import.
110. Monthus C., and Le Doussal P. Eur. Phys. J. B 41 (2004) 535 cond-mat/0407289
111. Kida S. J. Fluid Mech. 93 (1979) 337
112. J.P. Bouchaud, M. Mezard, cond-mat/9707047.
113. Derrida B., and Spohn H. J. Stat. Phys. 51 (1988) 817
114. Kardar M., Parisi G., and Zhang Y.C. Phys. Rev. Lett. 56 (1986) 889
115. Vanden Eijnden E.W.E. Phys. Fluids 11 (1999) 21492153 chao-dyn/9901006
116. Vanden Eijnden E.W.E. Phys. Fluids 12 (2000) 149154 chao-dyn/9901029
117. Vanden Eijnden E.W.E. Commun. Pure Appl. Math. 53 (2000) 852901 chao-dyn/9904028
118. C. Hagendorf, P. Le Doussal, 0803.3249.
119. P. Le Doussal, 0809.1192.