Order versus disorder in the quantum Heisenberg antiferromagnet on the kagomé lattice using exact spectra analysis

A group-symmetry analysis of the low-lying levels of the spin-1/2 kagomé Heisenberg antiferromagnet is performed for small samples up to $N=27\mathrm{}$. This approach allows one to follow the effect of quantum fluctuations when the sample size increases. The results contradict the scenario of “order by disorder” which has been advanced on the basis of large-$S$ calculations. A large enough second-neighbor ferromagnetic exchange coupling is needed to stabilize the $\sqrt{3}\times \sqrt{3}$ pattern: the finite-size analysis indicates a quantum critical transition at a nonzero coupling.