What is a simple explanation for the chayes-mckellar-winn theorem?

The Chayes-McKellar-Winn theorem provides a mathematical framework for understanding the behavior of certain statistical mechanics models, particularly in relation to the phase transitions of systems with long-range interactions. Specifically, it shows that under specific conditions, such as the presence of a phase transition, the behavior of the system can be described by a limiting free energy and that the associated equilibrium states exhibit a unique structure. This theorem is significant in the study of complex systems and helps clarify how microscopic interactions can lead to macroscopic phenomena.