  The Edwards-Wilkinson (EW) growth of $1+1$ interface is considered in the
background of the correlated random noise. We use random Coulomb potential as
the background long-range correlated noise. A depinning transition is observed
in a critical driving force $F_c\approx 0.37$ in the vicinity of which the
final velocity of the interface varies linearly with time. Our data collapse
analysis for the velocity shows a crossover time $t^*$ at which the velocity is
size independent. Based on a two-variable scaling analysis, we extract the
exponents, which are different from all universality classes we are aware of.
Especially noting that the dynamic and roughness exponents are $z_w=1.55\pm
0.05$, and $\alpha_w=1.05\pm 0.05$ at the criticality, we conclude that the
system is different from both EW and KPZ universality classes. Our analysis
shows therefore that making the noise long-range-correlated, drives the system
out of EW universality class. The simulations on the tilted lattice shows that
the non-linearity term ($\lambda$ term in the KPZ equations) goes to zero in
the thermodynamic limit.

Statistical Mechanics