Spin-Peierls Dimerization of a s=1/2 Heisenberg Antiferromagnet on a   Square Lattice
  Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is investigated for several possible dimerized configurations, some of which are shown to have lower ground state energies than the others. In particular, the lattice deformations resulting in alternate stronger and weaker couplings along both the principal axes of a square lattice are shown to result in a larger gain in magnetic 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 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 critical regime $(0\leq \delta \leq 0.1)$ as well as in the far regime $(0\leq \delta <1)$. It is suggested that the unexpanded exchange coupling is as much a source of the logarithmic dependence as a correction due to the contribution of umklapp 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 $\delta ^{x}$. 
Aiman Al-Omari