Finite-temperature functional RG, droplets and decaying Burgers turbulenceP. 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 ) 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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