The authors examine the nature of two-magnon excitations in the alternating bond ferromagnetic S=1/2 spin chain. Both a direct analytic approach as well as a method based on a scaling transformation are used to study the bound state branches and their relationship to the two-magnon continuum. Several features are expected to be observable in two-magnon Raman scattering experiments.

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All 8th order Franklin bent diagonal squares with distinct elements 1, …, 64 have been constructed by an exact backtracking method. Our count of 1, 105, 920 dramatically increases the handful of known examples, and is some eight orders of magnitude less than a recent upper bound. Exactly one-third of these squares are pandiagonal, and therefore magic. Moreover, these pandiagonal Franklin squares have the same population count as the eighth order ‘complete’, or ‘most-perfect pandiagonal magic’, squares. However, while distinct, both types of squares are related by a simple transformation. The situation for other orders is also discussed.