On the nature of the order parameter in quantum antiferromagnets

The first moments of the magnetization $m_z$ of the $d=2$, $S=1/2$ quantum Heinsenberg antiferromagnet with nearest neighbor interactions on the square lattice are computed for $T=0$ via path integral Monte Carlo Simulations. The results for the ratio $R=\langle m^4_z \rangle / \langle m^2_z \rangle^2$ show a cross-over at a system size of $N \approx 100$ to the classical behavior, $\lim_{N\to \infty} R = 9/5$. This supports the arguments that the long range order in the ground state is reached by a spontaneous symmetry breaking, just as in the classical case