Conditions for a ferromagnetic ground state of Ising and Heisenberg models. II. All Bravais lattices

For the isotropic Heisenberg Hamiltonian with ferromagnetic nearest- and antiferromagnetic next-nearest-neighbor interactions: $H=J_1{\Sigma }_{\left(\mathrm{nn}\right)}{\overrightarrow{\mathrm{S}}}_n{\overrightarrow{\mathrm{S}}}_{n+{\delta }_1}+J_2{\Sigma }_{\left(\mathrm{nnn}\right)}{\overrightarrow{\mathrm{S}}}_n{\overrightarrow{\mathrm{S}}}_{n+{\delta }_2}$, $J_1<0\mathrm{}$, $J_2>0\mathrm{}$, necessary and sufficient conditions for a ferromagnetic ground state are obtained for all Bravais lattices with periodic boundaries and arbitrary spin $s$. For some lattices, e.g., the cubic lattices in two and three dimensions, these conditions are spin dependent. For the Ising and classical Heisenberg model, the threshold values for $\frac{\left|J_1\right|}{J_2}$ are calculated and compared with the quantum case. The results are also consistent with most of the experimental information.