## Forthcoming article in JSTAT

Our article “Uniqueness of the thermodynamic limit for driven disordered elastic interfaces” has been accepted for publication in JSTAT.

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 $M=kL^\zeta$ with periodic boundary conditions, where $\zeta$ is the depinning roughness exponent and $k$ is a finite aspect ratio parameter. We focus on the crossover from the infinitely narrow ($k\to 0$) to the infinitely wide ($k\to \infty$) 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 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 $k$.

Longitudinal ﬁnite-size dependence of
the averaged critical force

Uniqueness of the thermodynamic limit for driven disordered elastic interfaces
A B Kolton, S Bustingorry, E E Ferrero and A Rosso
Provisionally scheduled for November 2013