We have studied the thickness-induced superconductor-to-insulator transition in the presence of a magnetic field for a-NbSi thin films. Analyzing the critical behavior of this system within the dirty boson model, we have found a critical exponents product of $ u_d z$ > 0.4. The corresponding phase diagram in the (H,d) plane is inferred. This small exponent product as well as the non-universal value of the critical resistance found at the transition call for further investigations in order to thoroughly understand these transitions.
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