Fully frustrated XY model with next-nearest-neighbor interaction

We investigate a fully frustrated XY model with nearest-neighbor (NN) and next-nearast-neighbor (NNN) couplings which can be realized in Josephson junction arrays. We study the phase diagram for 0 less than or equal to x less than or equal to 1 (x is the ratio between NNN and NN couplings). When x<1/root 2, an Ising transition and a Berezinskii-Kosterlitz-Thouless transition are present. Both critical temperatures decrease with increasing x. For x>1/root 2 the array undergoes a sequence of two transitions. On raising the temperature first the two sublattices decouple from each other and then, at higher temperatures, each sublattice becomes disordered, The structure of phase diagram remains the same if weak interaction with further neighbors is included.