Papers › Uniqueness of the thermodynamic limit for driven disordered elastic interfaces
Uniqueness of the thermodynamic limit for driven disordered elastic interfaces
A. B. Kolton, S. Bustingorry, E. E. Ferrero, A. Rosso
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We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size L displacing in a disordered medium of transverse size M=k L^ζ with periodic boundary conditions, where ζ is the depinning roughness exponent and k is a finite aspect ratio parameter. We focus on the crossover from the infinitely narrow (k→0) to the infinitely wide (k→∞) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behavior of the velocity-force characteristics are {\it unique} and k-independent. We also show that the finite size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of k. Our results are relevant for understanding anisotropic size-effects in force-driven and velocity-driven interfaces.
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