  We study detailed classical-quantum correspondence for a cluster system of
three spins with single-axis anisotropic exchange coupling. With autoregressive
spectral estimation, we find oscillating terms in the quantum density of states
caused by classical periodic orbits: in the slowly varying part of the density
of states we see signs of nontrivial topology changes happening to the energy
surface as the energy is varied. Also, we can explain the hierarchy of quantum
energy levels near the ferromagnetic and antiferromagnetic states with EKB
quantization to explain large structures and tunneling to explain small
structures.
