Diabolical points in magnetic molecules: An exactly solvable model

The magnetic molecule Fe₈ has a rich pattern of degeneracies in its magnetic spectrum as the static magnetic field applied to it is varied. The points of degeneracy, or diabolical points in the magnetic field space, are found exactly in the simplest model Hamiltonian for this molecule. They are shown to form a perfect centered rectangular lattice, and to be multiply diabolical in general. The multiplicity is found. An earlier semiclassical solution to this problem is thereby shown to be exact in leading order in $1/J$ where J is the spin.