We study the superconductor-insulator percolation threshold in a two-d
imensional system and provide experimental evidence for the non-univer
sality of the critical exponents for the critical current in two diffe
rent cases: evaporated thin lead films and ion milled thin lead films.
For evaporated films, the exponent measured was v = 1.88 +/- 0.09 and
for ion milled films v = 1.84 +/- 0.05. In both cases, we found criti
cal exponents greater than the exponents predicted for a discrete two-
dimensional lattice (v = 1.333) and that are consistent with continuum
percolation models and the microstructure of our films.