# Overlap, disorder, and directed polymers: A renormalization group approach.

@article{Mukherji1994OverlapDA,
title={Overlap, disorder, and directed polymers: A renormalization group approach.},
author={Mukherji},
journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
year={1994},
volume={50 4},
pages={
2407-2410
}
}
• Mukherji
• Published 25 November 1993
• Mathematics, Physics, Medicine
• Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
The overlap of a (d+1)-dimensional directed polymer of length t in a random medium is studied using a renormalization group approach. In d\ensuremath{\gtrsim}2 it vanishes at ${\mathit{T}}_{\mathit{c}}$ for t\ensuremath{\rightarrow}\ensuremath{\infty} as ${\mathit{t}}^{\mathrm{\ensuremath{\Sigma}}}$ where \ensuremath{\Sigma}=[(d-1)/(3-2d)](d/z) and z is the transverse spatial rescaling exponent. The same formula holds in d=1 for any finite temperature and it agrees with previous numerical…
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