Suppression of Dimer Correlations in the Two-Dimensional $J_1$-$J_2$ Heisenberg Model: an Exact Diagonalization Study

We present an exact diagonalization study of the ground state of the spin-half $J_1-J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results – especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established – suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter.