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Driven interface depinning in a disordered medium
Author(s) -
Leschhorn Heiko,
Nattermann Thomas,
Stepanow Semjon,
Tang LeiHan
Publication year - 1997
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19975090102
Subject(s) - physics , exponent , functional renormalization group , critical exponent , cusp (singularity) , isotropy , singularity , condensed matter physics , renormalization group , order (exchange) , langevin dynamics , phase transition , thermal fluctuations , langevin equation , dimension (graph theory) , mathematical physics , statistical physics , quantum mechanics , mathematical analysis , geometry , mathematics , combinatorics , philosophy , linguistics , finance , economics
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 F c ) θ for driving forces F close to its threshold value F c . 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 F c , 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.