Critical exponents and fine-grid vortex model of the dynamic vortex Mott transition in superconducting arrays

We study the dynamic vortex Mott transition in two-dimensional superconducting arrays in a magnetic field with $f$ flux quantum per plaquette. The transition is induced by external driving current and thermal fluctuations near rational vortex densities set by the value of $f$, and has been observed experimentally from the scaling behavior of the differential resistivity. Recently, numerical simulations of interacting vortex models have demonstrated this behavior only near fractional $f$. A fine-grid vortex model is introduced, which allows to consider both the cases of fractional and integer $f$. The critical behavior is determined from a scaling analysis of the current-voltage relation and voltage correlations near the transition, and by Monte Carlo simulations. The critical exponents for the transition near $f=1/2$ are consistent with the experimental observations and previous numerical results from a standard vortex model. The same scaling behavior is obtained for $f=1$, in agreement with experiments. However, the estimated correlation-length exponent indicates that even at integer $f$, the critical behavior is not of mean-field type.