Directed polymers in high dimensions

Details Directed polymers in high dimensions Directed polymers in high dimensions

1996-02-08

arxiv.org/abs/cond-mat/9602045v1

Physics

Condensed Matter

37 pages REVTEX including 4 PostScript figures

Scientific paper

10.1103/PhysRevE.54.304

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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