  We calculate the tunnelling resistance at the quantum critical point of a
mesoscopic SQUIDs array in the presence of magnetic flux. We find the
analytical relation between the magnetic flux induced dissipation strength and
the Luttinger liquid parameter of the system. While the experimental finding
for the system is around 40-50 mK, we find the behavior of the system even at
lower temperatures through the analysis of renormalization group. Apart from
the length scale dependent superconductor-insulator transition, we also predict
the evidence of length scale independent metallic state. This study also
emphasizes the importance of Co-tunelling effect.
