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It has previously been pointed out that the coexistence of infinite-range andshort-range interactions causes a system to have a phase transition of themean-field universality class, in which the cluster size is finite even at thecritical point. In the present paper, we study this property in a model ofbistable molecules, whose size changes depending on the bistable states. Themolecules can move in space, interacting via an elastic interaction. It isknown that due to the different sizes, an effective long-range interactionbetween the spins appears, and thus this model has a mean-field type of phasetransition. It is found that the scaling properties of the shift of thecritical temperature from the pure short-range limit in the model withinfinite-range and short-range interactions hold also in the present model,regarding the ratio of the size of the two states as a control parameter forthe strength of the long-range interaction. By studying the structure factor,it is shown that the dependence of the cluster size at the critical temperaturealso shows the same scaling properties as a previously studied model with bothinfinite-range and short-range interactions. We therefore conclude that thesescaling relations hold universally in hybrid models with both short-range andweak long-range interactions.

Critical temperature and correlation length of an elastic interaction model for spin-crossover materials