CONDITIONS FOR A FERROMAGNETIC GROUND-STATE OF HEISENBERG HAMILTONIANS

For isotropic Heisenberg Hamiltonians with ferromagnetic nearest and anitferromagnetic next-nearest neighbor interactions, H=J1(nn) S→n•S→n+δ1+J2(nnn)S→n•S→n+δ2, J1<0,J2>0 the following conditions for a ferromagnetic ground state are derived. With periodic boundary conditions it is necessary that we have |J1|J2>4cos2(πN),2,4 for the simple-cubic lattice in one, two, and three dimensions, respectively. For periodic and for open boundaries it is sufficient that we have |J1|J2>4.2+1s, and 4+2s in the three cases. © 1979 The American Physical Society.