Abstract
Order–disorder phenomena in alloys and magnetic crystals can be discussed by statistical mechanics in mean-field accuracy, for which the lattice structure is assumed as insignificant. Statistical theories deal with essential features of ordering, although some details are left unexplained in the mean-field approximation. It is a serious drawback of mean-field theories that we cannot deal with the symmetry change that characterizes structural phase transitions in a crystal. Nevertheless, existing theories are reviewed in this chapter, realizing that probabilities are an important concept for order–disorder phenomena. In any case, the mean-field theory is basically inappropriate for long-range interactions, unless crystals are characterized by uniform densities.
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