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There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.

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The following questions are considered: How do itinerant d electrons of the Heusler alloys produce magnetic moments that are completely localized on the Mn atoms? What is the microscopic origin of Invar anomalies? Why is elemental antiferromagnetism confined to Cr, Mn, and Fe? Why do the Fe atoms in Fe3Si carry two distinctly different magnetic moments? Can we use our understanding of transiton-metal magnetism to ’’design’’ new magnetic compounds composed of nonmagnetic elements? Our answers to these questions are based on the local-spin-density theory of electronic exchange and correlation, implemented using parameter-free self-consistent energy-band calculations.

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