  Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is
investigated by taking unexpanded exchange couplings. Several dimerized
configurations are considered some of which are shown to have lower ground
state energies than others. In particular, the lattice deformations resulting
in alternate strong and weak couplings along both the principal axes of a
square lattice are shown to result in a larger gain in energy. In addition, a
`columnar' configuration is shown to have a lower ground state energy and a
faster increase in the energy gap parameter than a `staggered' configuration.
The inclusion of unexpanded exchange coupling leads to a power law behaviour
for the magnetic energy gain and the spin-Peierls gap, which is qualitatively
different from that reported earlier. Instead of varying as $\delta ^x$, the
two quantities are shown proportional to $\delta ^\nu / |ln \delta|.$ It is
thus proposed that the logarithmic correction, that was regarded as an outcome
of including umklapp processes for small distortions, can also be a direct
consequence of using an un-truncated spin-spin exchange interaction. The
calculations, which employ the coupled cluster method, lead to a conclusion
result that the dimerization of a spin-half Heisenberg antiferromagnet on a
sqaure lattice is unconditional.
