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

TL;DR

This paper investigates the critical temperature and correlation length in an elastic interaction model for spin-crossover materials, demonstrating universal scaling relations in hybrid systems with short-range and weak long-range interactions.

Contribution

It introduces a model where elastic interactions induce effective long-range interactions, and shows that scaling properties at criticality are universal across similar hybrid models.

Findings

Critical temperature shift follows known scaling laws.

Cluster size at criticality exhibits universal scaling behavior.

Scaling relations hold for models with weak long-range interactions.

Abstract

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.