Polymers in quenched random environment: Weak replica symmetry breaking

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Abstract
The case of polymers in strong quenched disorder is investigated. The disorder is modeled by a quenched random potential which is sampled by a flexible polymer chain. It is shown that the problem, originally formulated in terms of Edwards type path integrals, can be transformed into an effective field theory. Localized phases of the polymer, where the size of the chain is independent of its contour length, i.e. R2∝(1/Δ)2/(4−d), can be found by a weak breaking of the replica symmetry. Δ is a measure for the disorder. The same formalism predicts at d=4 an essential singularity R2 ∝exp(2π2/Δ) for vanishing disorder Δ→0.

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