Monte Carlo studies of percolation in a superconducting array

We investigate phase transitions in a two-dimensional site-diluted superconducting array, using Monte Carlo simulations. The array is modeled via a site-diluted classical XY model on a square lattice in the regime pc<p<1, where p is the concentration of spins (representing the phases of the superconducting order parameters on the grains) and pc denotes the percolation threshold. In the unfrustrated case (zero magnetic field), we find that the Kosterlitz-Thouless (KT) transition temperature Tc(p) approaches zero according to the power law Tc(p)(p-pc) and 1.14, as p'pc from above. To within the accuracy of the calculation, equals the expected value of t, where t1.30 is the usual conductivity exponent. In the fully frustrated case, which in a perfect lattice (p=1) is characterized by a phase transition of combined KT- and Ising-like character, we find no Ising-like character in the diluted lattice. The apparent KT behavior is broadened over a considerable temperature range, compared to the case in the perfect lattice. © 1991 The American Physical Society.