  We study the phase diagram of an elastic interaction model for spin crossover
(SC) materials with antiferromagnetic-like short-range interactions. In this
model, the interplay between the short-range interaction and the long-range
interaction of elastic origin causes complex phase transitions. For relatively
weak elastic interactions, the phase diagram is characterized by tricritical
points, at which antiferromagnetic (AF) -like and ferromagnetic (F) -like
spinodal lines and a critical line merge. On the other hand, for relatively
strong elastic interactions, unusual "horn structures," which are surrounded by
the F-like spinodal lines, disorder (D) spinodal lines, and the critical line,
are realized at higher temperatures. These structures are similar to those
obtained in our previous study [Phys. Rev. B {\bf 93}, 064109 (2016)] of an
Ising antiferromagnet with infinite-range ferromagnetic interactions, and we
find universal features caused by the interplay between the competing
short-range and long-range interactions. The long-range interaction of elastic
origin is irrelevant (inessential) for the critical line. In contrast, the
AF-like, F-like, and D spinodal lines result from the long-range interaction of
elastic origin. This difference causes qualitatively different features of
domain formation or nucleation of the new phase: clustering occurs in the
former case, while clustering is absent in the latter. Based on the phase
diagrams, we discuss the patterns and clustering features of two-step SC
transitions, in which the AF-like phase is realized in the intermediate
temperature region.
