  In spin-crossover materials, the volume of a molecule changes depending on
whether it is in the high-spin (HS) or low-spin (LS) state. This change causes
distortion of the lattice. Elastic interactions among these distortions play an
important role for the cooperative properties of spin-transition phenomena. We
find that the critical behavior caused by this elastic interaction belongs to
the mean-field universality class, in which the critical exponents for the
spontaneous magnetization and the susceptibility are $\beta = 1/2$ and $\gamma
= 1$, respectively. Furthermore, the spin-spin correlation function is a
constant at long distances, and it does not show an exponential decay in
contrast to short-range models. The value of the correlation function at long
distances shows different size-dependences: $O(1/N)$, $O(1/\sqrt{N})$, and
constant for temperatures above, at, and below the critical temperature,
respectively. The model does not exhibit clusters, even near the critical
point. We also found that cluster growth is suppressed in the present model and
that there is no critical opalescence in the coexistence region. During the
relaxation process from a metastable state at the end of a hysteresis loop,
nucleation phenomena are not observed, and spatially uniform configurations are
maintained during the change of the fraction of HS and LS. These
characteristics of the mean-field model are expected to be found not only in
spin-crossover materials, but also generally in systems where elastic
distortion mediates the interaction among local states.
