PMID: 15244545Jul 13, 2004Paper

Directed polymers and interfaces in random media: free-energy optimization via confinement in a wandering tube

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Cécile Monthus, Thomas Garel

Abstract

We analyze, via Imry-Ma scaling arguments, the strong disorder phases that exist in low dimensions at all temperatures for directed polymers and interfaces in random media. For the uncorrelated Gaussian disorder, we obtain that the optimal strategy for the polymer in dimension 1+d with 0<d<2 involves at the same time (i) a confinement in a favorable tube of radius R(S) approximately L (nu(S) ) with nu(S) =1/(4-d)<1/2 (ii) a superdiffusive behavior R approximately Lnu with nu=(3-d)/(4-d)>1/2 for the wandering of the best favorable tube available. The corresponding free energy then scales as F approximately Lomega with omega=2nu-1 and the left tail of the probability distribution involves a stretched exponential of exponent eta=(4-d)/2. These results generalize the well known exact exponents nu=2/3, omega=1/3, and eta=3/2 in d=1, where the subleading transverse length R(S) approximately L(1/3) is known as the typical distance between two replicas in the Bethe ansatz wave function. We then extend our approach to correlated disorder in transverse directions with exponent alpha and/or to manifolds in dimension D+d= d(t) with 0<D<2. The strategy of being both confined and superdiffusive is still optimal for decaying correlations ( al...Continue Reading

References

Apr 15, 1990·Physical Review. a·B Derrida, O Golinelli
Aug 15, 1991·Physical Review. a·J M KimA J Bray
Aug 15, 1991·Physical Review. a·C K PengH E Stanley
Feb 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·N N Pang, T Halpin-Healy
Aug 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C H Lam, L M Sander
Sep 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T Halpin-Healy, D Herbert
Feb 1, 1996·Physical Review. B, Condensed Matter·T GarelH Orland
Sep 1, 1990·Physical Review. B, Condensed Matter·Y C Zhang
May 1, 1991·Physical Review. B, Condensed Matter·D S Fisher, D A Huse
Feb 1, 1994·Physical Review. B, Condensed Matter·T Hwa, D S Fisher
Jun 24, 1985·Physical Review Letters·D A Huse, C L Henley
Dec 23, 1985·Physical Review Letters·D A HuseD S Fisher
May 18, 1987·Physical Review Letters·M Kardar, Y C Zhang
Nov 9, 1987·Physical Review Letters·Y C Zhang
Aug 29, 1988·Physical Review Letters·M V Feigel'man, V M Vinokur
Jan 23, 1989·Physical Review Letters·T Halpin-Healy
Apr 15, 1991·Physical Review Letters·H G Hentschel, F Family
Dec 7, 1992·Physical Review Letters·C H Lam, L M Sander
Sep 16, 2000·Physical Review Letters·M Prahofer, H Spohn
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·E Brunet, B Derrida
Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·X H WangM Schwartz
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E T SeppäläP M Duxbury
Aug 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marta Sales, Hajime Yoshino

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Citations

Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Oppermann, M J Schmidt
May 10, 2020·Polymers·Róbinson J Acosta DiazNami F Svaiter
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I V Kolokolov, S E Korshunov
Mar 21, 2008·Physical Review Letters·V S DotsenkoG Blatter
Aug 7, 2007·Physical Review Letters·L Canet, M A Moore

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