Journal
EUROPHYSICS LETTERS
Volume 76, Issue 3, Pages 457-463Publisher
IOP Publishing Ltd
DOI: 10.1209/epl/i2006-10295-1
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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 similar to 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.
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