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Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice isinvestigated for several possible dimerized configurations, some of which areshown to have lower ground state energies than the others. In particular, thelattice deformations resulting in alternate stronger and weaker couplings alongboth the principal axes of a square lattice are shown to result in a largergain in magnetic energy. In addition, a `columnar' configuration is shown tohave a lower ground state energy and a faster increase in the energy gapparameter than a `staggered' configuration. The inclusion of unexpandedexchange coupling leads to a power law behaviour for the magnetic energy gainand energy gap, which is qualitatively different from that reported earlier.Instead of increasing as $\delta ^{x}$, the two quantities depend on $\delta $as $\delta ^{\nu}/| \ln \delta | .$ This is true both in the near criticalregime $(0\leq \delta \leq 0.1)$ as well as in the far regime $(0\leq \delta<1)$. It is suggested that the unexpanded exchange coupling is as much a sourceof the logarithmic dependence as a correction due to the contribution ofumklapp processes. Staggered magnetization is shown to follow the same $\delta$-dependence in all the configurations in the small $\delta $-regime, while for$0\leq \delta <1$, it follows the power law $\delta ^{x}$.Comment: 12 pages, 7 Postscript figures, RevTex forma

Spin-Peierls Dimerization of a \(\mib{s}=\frac{{\bf 1}}{{\bf 2}}\) Heisenberg Antiferromagnet on a Square Lattice