- Autor(in)
- Referenz
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- Seitenbereich
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0001 - 0034
- Schlagwort(e)
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<KWD>Disorder
Interfaces
Nonequilibrium phase transitions
- Zusammenfsg.
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The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity <I>v</I>, which increases as <I>v</I> ~(<I>F</I> <I>F</I><sub><I>c</I></sub>)<sup>θ</sup> for driving forces <I>F</I> close to its threshold value <I>F</I><sub><I>c</I></sub>. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical exponents characterizing the depinning transition are obtained to the first order in ε = 4 - <I>D</I> > 0, where <I>D</I> is the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France <B>2</B> (1992) 1483]. Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold <I>F</I><sub><I>c</I></sub>, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For ε = 1 the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions ε = 2, 3 are larger and suggest that the roughness exponent is somewhat larger than the value ξ = <I>e</I>/3 of an interface in thermal equilibrium.
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- Forschungsartikel