We show that the mean-field theory of quantum Heisenberg models introduced by Arovas and Auerbach predicts long-range order for all dimensions $d\ge 2$ in the ground state as well as below a critical temperature $T_c\mathrm{}\left(d\right)\mathrm{}$ that is nonzero for $d>\mathrm{}2\mathrm{}$. The long-range order in the ground state is the same as predicted by conventional spin-wave theory.

• Received 26 September 1988

DOI:https://doi.org/10.1103/PhysRevB.39.2850