The fate of the elastic string: roughening near the depinning threshold

Simulations of an elastic string in 1+1 dimensions near and at the depinning threshold f c are presented. The spatial dependence of the roughness is characterized by two exponents. One, eta approximately=0.9, describes the height-height correlations. The other, chi approximately=1.15, measures how the transverse width, W, of the string increases with increasing string length. Since chi >1 any physical string will eventually break as its length is increased. The growth of the width of the string with time is controlled by an exponent beta approximately=0.9. As the applied driving force approaches f c from above the width increases according to W approximately (f-f c ) - sigma with sigma approximately=. The dependence of f c on the strength of the random potential is found to be in agreement with the collective pinning theory by Larkin and Ovchinnikov (1979).