This study makes contact with optimization theory at two places. First, the spin problem is initially expressed as an application of Hamiltonian dynamics; that is, it is simply an explicit particular example of the principle of least action. In the course of solution, we uncover two qualitatively different types of behavior, viz ‘regular’ and ‘chaotic,’ whose occurrence depends on the value of a (control) parameter. The chaotic solutions, moreover, are not equally chaotic; there is a more-or-less smooth progression into and back out of chaos as the parameter changes. The second contact with control theory then is a question; can the ‘intensity’ of the chaos be quantified, and if so, is there a value of the parameter for which the system is maximally chaotic?

The paper has four sections. Section 2 is a review of classical dynamics, including a description of numerical techniques for distinguishing regular from chaotic motion. Section 3 describes how the quantum mechanical form of a classical dynamics problem is produced. Section 4 discusses the exchange-type interactions relevant to classical spins and presents results of numerical integration for one specific such model.

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