  Recent numerical and analytical work has shown that for the square-lattice
Heisenberg model the boundary can induce Dimer correlations near the edge which
are absent in spin-wave theories and non-linear sigma model approaches. Here,
we calculate the nearest-neighbor spin correlations parallel and perpendicular
to the boundary in a semi-infinite system for two different square-lattice
Heisenberg models: (i) A frustrated $J_1-J_2$ model with nearest and second
neighbor couplings and (ii) a spatially anisotropic Heisenberg model, with
nearest-neighbor couplings $J$ perpendicular to the boundary and $J^\prime$
parallel to the boundary. We find that in the latter model, as $J^\prime/J$ is
reduced from unity the Dimer correlations near the edge become longer ranged.
In contrast, in the frustrated model, with increasing $J_2$, dimer correlations
are strengthened near the boundary but they decrease rapidly with distance.
These results imply that deep inside the N\'{e}el phase of the $J_1-J_2$
Heisenberg model, dimer correlations remain short-ranged. Hence, if there is a
direct transition between the two it is either first order or there is a very
narrow critical region.
