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Evolution of the thermodynamic properties and inelastic neutron scattering intensities for spin-1/2 antiferromagnetic quantum rings

This study examines the increasing complexity in the magnetic properties of small $n$ = 3, 4, 5, 6 spin-1/2 quantum rings. Using an exact diagonalization of the isotropic Heisenberg Hamiltonian with nearest and next-nearest neighbor interactions, the energy eigenstates, magnetic specific heat capacity, magnetic susceptibility, and inelastic neutron scattering structure factors are determined for variable next-nearest neighbor interactions. Here, it is shown that the presence of a complex spin-mixing, multiple ground states, and non-zero ground states greatly complicate the spin Hamiltonian. Overall, the energy eigenstates and structure factor intensities are presented in closed form, while the thermodynamic properties detail the effect of a crossing interaction in the rings. The goal of this work is to provide insight into the evolution of the magnetic properties and spin excitations within these systems.