  We study the nature of the ground state of the frustrated J1-J2 model and the
J1-J3 model using a variational algorithm based on projected entangled-pair
states (PEPS). By investigating spin-spin correlation functions, we observe a
separation in regions with long-range and short-range order. A direct
comparison with exact diagonalizations in the subspace of short-range valence
bond singlets reveals that the system is well described by states within this
subset in the short-range order regions. We discuss the question whether the
system forms a spin-liquid, a plaquette valence bond crystal or a columnar
dimer crystal in these regions.
