Using Monte Carlo simulations we have investigated the critical behavior of the classical fully frustrated XY model in two dimensions in a square lattice. There are two phase transitions in the model, one of the Berezinskii-Kosterlitz-Thouless type and a Z2 transition at higher temperature. We show that the vortex anti-vortex density has a clear signature of the Z2 phase transition at exactly the percolation threshold.
