Néel order in the two-dimensional $S=\frac{1}{2}$ Heisenberg model

The existence of Néel order in the $S=1∕2$ Heisenberg model on the square lattice at $T=0$ is shown using inequalities set up by Kennedy, Lieb, and Shastry in combination with high-precision quantum Monte Carlo data.

Figure 1

(Color online) Bound on $\overline{g}\left(n\right)$ obtained from Eq. (9) and $\overline{g}\left(n\right)$ for $24\times 24$, $36\times 36$, and $40\times 40$ lattices at $T=0.025$ versus $n$.