| Issue |
EPL
Volume 90, Number 2, April 2010
|
|
|---|---|---|
| Article Number | 20003 | |
| Number of page(s) | 5 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/90/20003 | |
| Published online | 13 May 2010 | |
Bethe ansatz derivation of the Tracy-Widom distribution for one-dimensional directed polymers
LPTMC, Université Paris VI - 75252 Paris, France, EU and L.D. Landau Institute for Theoretical Physics - 119334 Moscow, Russia
Corresponding author: dotsenko@lptmc.jussieu.fr
Received:
29
March
2010
Accepted:
8
April
2010
The distribution function of the free-energy fluctuations in one-dimensional directed polymers with δ-correlated random potential is studied by mapping the replicated problem to a many-body quantum boson system with attractive interactions. Performing the summation over the entire spectrum of excited states the problem is reduced to the Fredholm determinant with the Airy kernel which is known to yield the Tracy-Widom distribution.
PACS: 05.20.-y – Classical statistical mechanics / 75.10.Nr – Spin-glass and other random models / 61.41.+e – Polymers, elastomers, and plastics
© EPLA, 2010
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