Finite-temperature functional RG, droplets and decaying Burgers turbulence

P. Le Doussal

doi:10.1209/epl/i2006-10295-1

All issues

Volume 76 / No 3 (November 2006)

Europhys. Lett., 76 3 (2006) 457-463

Abstract

Issue		Europhys. Lett. Volume 76, Number 3, November 2006


Page(s)		457 - 463
Section		Condensed matter: structural, mechanical and thermal properties
DOI		https://doi.org/10.1209/epl/i2006-10295-1
Published online		11 October 2006

Europhys. Lett., 76 (3), pp. 457-463 (2006)

Finite-temperature functional RG, droplets and decaying Burgers turbulence

P. Le Doussal

CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure 24 Rue Lhomond, 75231 Paris, France

Received: 20 May 2006
Accepted: 18 September 2006

Abstract

The functional RG (FRG) approach to pinning of d-dimensional manifolds is re-examined at any temperature T. The coupling function $R(u)$ is shown to be a physical observable in any d, exactly related to a free energy cumulant in a parabolic well. In $d=0$ its beta function is displayed to a high order, ambiguities resolved; for random field disorder (Sinai model) we obtain exactly the $T=0$ fixed point $R(u)$ and its thermal boundary layer (TBL) form (i.e. for $u \sim T$ ) at $T>0$ . Connection between FRG in $d=0$ and decaying Burgers turbulence is discussed. An exact solution to the functional RG hierarchy in the TBL is obtained for any d and related to droplet probabilities.

PACS: 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions

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