Probability distribution of the free energy of a directed polymer in a random medium

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

Volumn 61, Issue 6 B, 2000, Pages 6789-6801

  Brunet, Éric ^a   Derrida, Bernard ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

GROUND STATE; INTEGRAL EQUATIONS; PERTURBATION TECHNIQUES; POLYMERS; PROBABILITY DISTRIBUTIONS; QUANTUM THEORY;

ASYMMETRIC EXCLUSION PROCESS; GROUND STATE ENERGY; KARDAR-PARISI-ZHANG EQUATION;

FREE ENERGY;

ASYMMETRIC EXCLUSION PROCESS; GROUND-STATE ENERGIES; INTERACTING PARTICLES; KARDAR-PARISI-ZHANG EQUATIONS; PARTITION FUNCTIONS; PER UNIT LENGTH; RANDOM MEDIUM; SCALING FORMS;

EID: 0034207254     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.6789     Document Type: Article

References (34)

1. M. Kardar and Y.-C. Zhang, Phys. Rev. Lett. 58, 2087 (1987).
2. Y.-C. Zhang, Phys. Rev. Lett. 59, 2125 (1987).
3. T. Halpin-Healy and Y.-C. Zhang, Phys. Rep. 254, 215 (1995).
4. B. Derrida and H. Spohn, J. Stat. Phys. 51, 817 (1988).
5. B. Derrida, Phys. Scr. T38, 6 (1991).
6. M. Mezard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
7. J. Z. Imbrie and T. Spencer, J. Stat. Phys. 52, 609 (1988).
8. M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986).
9. J. Krug, Adv. Phys. 46, 139 (1997).
10. M. Kardar, Nucl. Phys. B 290 [FS20], 582 (1987).
11. B. Derrida and J. L. Lebowitz, Phys. Rev. Lett. 80, 209 (1998).
12. B. Derrida and C. Appert, J. Stat. Phys. 94, 1 (1999).
13. D. Kim, Phys. Rev. E 52, 3512 (1995).
14. D.-S. Lee and D. Kim, Phys. Rev. E 59, 6476 (1999).
15. J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 333 (1999).
16. C. Appert, Phys. Rev. E 61, 2092 (2000).
17. E. Brunet and B. Derrida, Physica A 279, 398 (2000).
18. E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).
19. E. H. Lieb, Phys. Rev. 130, 1616 (1963).
20. C. N. Yang and C. P. Yang, J. Math. Phys. 10, 1115 (1969).
21. M. Gaudin, Phys. Rev. A 4, 386 (1971).
22. M. Jimbo, T. Miwa, Y. Môri, and M. Sato, Physica D 1, 80 (1980).
23. H. B. Thacker, Rev. Mod. Phys. 53, 253 (1981).
24. M. Gaudin, La Fonction d'Onde de Bethe (Masson, Paris, 1983).
25. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (CUP, Cambridge, 1927).
26. M. Praehofer and H. Spohn, Phys. Rev. Lett. (to be published) (e-print cond-mat/9910273).
27. K. Johansson, Commun. Math. Phys. 209, 437 (2000).
28. J. M. Kim, M. A. Moore, and A. J. Bray, Phys. Rev. A 44, 2345 (1991).
29. T. Halpin-Healy, Phys. Rev. A 44, R3415 (1991).
30. J. Krug, P. Meakin, and T. Halpin-Healy, Phys. Rev. A 45, 638 (1992).
31. J. L. Cardy, J. Phys. A 17, 385 (1984).
32. J. Mathews and R. L. Walker, Mathematical Methods of Physics (Addisson-Wesley, Reading, MA, 1973).
33. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1972).
34. G. Szegö, Orthogonal Polynomials, No. 23 in Colloquium Publications (AMS, New York, 1959).