The critical behavior of two-dimensional Josephson-junction network with the positional disorder is studied via Monte Carlo simulations. We consider a two-band model in which each superconducting grain is randomly displaced from its ideal position on a square lattice and the effective strength of the disorder is controlled by tuning the magnitude of transverse magnetic field. With the finite-size scaling analysis, we determine the phase diagram of this system as a function of disorder and temperature. In the weak disorder regime, our numerical results demonstrate the emergence of multiple Berezinskii-Kosterlitz-Thouless-type phase transitions from the normal to two different superconducting states. The new intermediate superconducting phase characterized by the quasi-long-range order exclusively in one of these bands will vanish when the disorder strength exceeds the critical value $f_c\approx 100$. Meanwhile in the strong disorder regime, our numerical data on the Edwards-Anderson order parameter support a zero-temperature transition from the normal state to the glassy phase.

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• Impurities in superconductors
• Multiband superconductivity
• Phase diagrams
• Phase transitions
• Unconventional superconductors
• Monte Carlo methods