Directed polymers subject to quenched external impurities (as in a polyelectrolyte in a gel matrix) are examined analytically, and numerically. Transverse fluctuations |x| scale with the length t of the polymer as |x|~t^ν. In all dimensions, for sufficiently strong disorder, ν can be different from the random-walk value of {}. Extensive numerical simulations in two, three, and four dimensions in fact suggest a superuniversal exponent of ν=2/3. The importance of the tree structure of the polymer ensemble is emphasized.
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Kardar et al. (1987) studied this question.
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