Universal depinning force fluctuations of an elastic line: Application to finite temperature behavior

The depinning of an elastic line in a random medium is studied via an extremal model. The latter gives access to the instantaneous depinning force for each successive conformation of the line. Based on conditional statistics the universal and non-universal parts of the depinning force distribution can be obtained. In particular the singular behavior close to a (macroscopic) critical threshold is obtained as a function of the roughness exponent of the front. We show moreover that the advance of the front is controlled by a very tenuous set of subcritical sites. Extension of the extremal model to a finite temperature is proposed, the scaling properties of which can be discussed based on the statistics of depinning force at zero temperature.