Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-10-29
Physical Review Letters 93, 015901 (2004)
Physics
Condensed Matter
Disordered Systems and Neural Networks
four pages, revtex4; minor modifications in the text and typos corrected
Scientific paper
10.1103/PhysRevLett.93.015901
The responses of a $1+\epsilon $ dimensional directed path to temperature and to potential variations are calculated exactly, and are governed by the same scaling form. The short scale decorrelation (strong correlation regime) leads to the overlap length predicted by heuristic approaches; its temperature dependence and large absolute value agree with scaling and numerical observations. Beyond the overlap length (weak correlation regime), the correlation decays algebraically. A clear physical mechanism explains the behavior in each case: the initial decorrelation is due to `fragile droplets,' which contribute to the entropy fluctuations as $\sqrt{T}$, while the residual correlation results from accidental intersections of otherwise uncorrelated configurations.
Bouchaud Jean-Philippe
da Silveira Rava A.
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