Superconducting-normal phase boundary of quasicrystalline arrays in a magnetic field

We study the effect of frustration, induced by a magnetic field, on the superconducting diamagnetic properties of two-dimensional quasicrystalline arrays. In particular, we calculate the superconducting-normal phase boundary, $T_c\mathrm{}\left(H\right)\mathrm{}$, for several geometries with quasicrystalline order. The agreement between our theoretically obtained phase boundaries and the experimentally obtained ones is very good. We also propose a new way of analyzing the overall and the fine structure of $T_c\mathrm{}\left(H\right)\mathrm{}$ in terms of short- and long-range correlations among tiles.