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