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Overlap, Disorder and Directed Polymers: A Renormalization Group Approach -

Sutapa Mukherji
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Abstract

The overlap of a $d+1$ dimensional directed polymer of length $t$ in a random medium is studied using a Renormalization Group approach. In $d>2$ it vanishes at $T_c$ for $t\rightarrow \infty$ as $t^Σ$ where $Σ=[\frac{d-1}{3-2d}]\frac{d}{z}$ 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 simulations at $d=1$. Among other results we also determine the scaling exponent for mutual repulsion of two chains in the random medium.

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Sutapa Mukherji. 1993-11-25. Overlap, Disorder and Directed Polymers: A Renormalization Group Approach -. https://doi.org/10.1103/physreve.50.r2407

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