We examined the eigenstates of the Heisenberg spin Hamiltonian (H) over cap=-J (S) over cap (1).(S) over cap (2) and the Ising spin Hamiltonian H-Ising=-J (S) over cap (1z)(S) over cap (2z) for a general spin dimer consisting of M unpaired spins at one spin site and N unpaired spins at the other spin site, and then analyzed how the broken-symmetry spin state of a spin dimer is related to the eigenstates of (H) over cap and (H) over cap (Ising). Our work shows that the description of the highest-spin and broken-symmetry spin states of a spin dimer by (H) over cap is the same as that by (H) over cap (Ising). For the analysis of spin exchange interactions of a magnetic solid on the basis of density functional theory, the use of the Heisenberg spin Hamiltonian in the "cluster" approach is consistent with that of the Ising spin Hamiltonian in the "noncluster" approach. (C) 2003 American Institute of Physics.