Abstract
We study the directed polymer in random media with an attractive line defect at the center of a three-dimensional substrate in d=3+1. It is found that a small defect strength of ϵ<ϵc does not make the polymer localized, whereas the defect strength of ϵ>ϵc restricts the polymer fluctuation to a finite region, suggesting that the critical strength ϵc is nonzero but finite. A localization transition appears at ϵc, where various critical exponents characterizing the polymer dynamics are also calculated.
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