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Canet, L.; Moore, M. A.

Universality classes of the Kardar-Parisi-Zhang equation. (English) Zbl 1228.82068

Phys. Rev. Lett. 98, No. 20, Article ID 200602, 4 p. (2007).
Summary: We reexamine mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling limit and show that there exist two branches of solutions. One branch (or universality class) exists only for dimensionalities \(d<d_c=2\) and is similar to that found by a variety of analytic approaches, including replica symmetry breaking and Flory-Imry-Ma arguments. The second branch exists up to \(d_c=4\) and gives values for the dynamical exponent \(z\) similar to those of numerical studies for \(d\geq2\).

Cited in 2 Documents

MSC:

82C27 Dynamic critical phenomena in statistical mechanics
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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