Inelastic neutron scattering from a geometrically frustrated Ising antiferromagnet: Exact solutions

Employing transformations of planar Ising models (decoration-decimation followed by star-triangle), the frustrated antiferromagnetic kagomé Ising model is mapped to the known disordered region of the ferromagnetic triangular Ising model. Thereafter, with supplemental aid of mapping theorems and linear algebraic correlation identities, correlations in the frustrated kagomé Ising model are determined at all temperatures, enabling exact solutions to be obtained in the neutron scattering problem. More particularly, the scattering function $S^{xx}(\vec{q},\omega )$ is uniform in momentum $\vec{q}$ and exhibits Dirac $\delta$ functions at select scattering frequencies, where each select frequency is associated with a temperature-dependent scattering amplitude. The scattering solutions are compared with those of the ferromagnetic kagomé Ising model.