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We present numerical exact results for the ground state and the low-lyingexcitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite squarelattices of up to N=40 sites. Using finite-size extrapolation we determine theground-state energy, the magnetic order parameters, the spin gap, the uniformsusceptibility, as well as the spin-wave velocity and the spin stiffness asfunctions of the frustration parameter J2/J1. In agreement with the generallyexcepted scenario we find semiclassical magnetically ordered phases for J2 <J2^{c1} and J2 > J2^{c2} separated by a gapful quantum paramagnetic phase. Weestimate J2^{c1} \approx 0.35J1 and J2^{c2} \approx 0.66J1.

The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins