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Directed polymers in high dimensions

Ralf Bundschuh·Michael Lassig
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Abstract

We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation theory we show that physical quantities develop singular behavior for d to 4. For example, the universal finite size amplitude of the free energy at the roughening transition is proportional to (4-d)^(1/2). This shows that the dimension d=4 plays a special role for this system and points towards d=4 as the upper critical dimension of the Kardar-Parisi-Zhang problem.

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Ralf Bundschuh, Michael Lassig. 1996-02-08. Directed polymers in high dimensions. https://doi.org/10.1103/physreve.54.304

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