TY - JOUR
T1 - Driven interface depinning in a disordered medium
AU - Leschhorn, Heiko
AU - Nattermann, Thomas
AU - Stepanow, Semjon
AU - Tang, Lei-Han
N1 - Publisher copyright:
© 1997 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 1997
Y1 - 1997
N2 - 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 v, which increases as v ∼(F Fc)θ for driving forces F close to its threshold value Fc. 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 — D > 0, where D is the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France 2 (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 Fc, 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 = e/3 of an interface in thermal equilibrium.
AB - 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 v, which increases as v ∼(F Fc)θ for driving forces F close to its threshold value Fc. 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 — D > 0, where D is the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France 2 (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 Fc, 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 = e/3 of an interface in thermal equilibrium.
KW - Disorder
KW - Interfaces
KW - Nonequilibrium phase transitions
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0030705043&partnerID=MN8TOARS
U2 - 10.1002/andp.19975090102
DO - 10.1002/andp.19975090102
M3 - Article
VL - 509
SP - 1
EP - 34
JO - Annalen der Physik (Leipzig)
JF - Annalen der Physik (Leipzig)
IS - 1
ER -