Europhys. Lett.
Volume 76, Number 3, November 2006
Page(s) 457 - 463
Section Condensed matter: structural, mechanical and thermal properties
Published online 11 October 2006
Europhys. Lett., 76 (3), pp. 457-463 (2006)
DOI: 10.1209/epl/i2006-10295-1

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 in final form 18 September 2006
published online 11 October 2006

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.

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

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