Cluster Property for Generalized Correlation Functions of Spin Systems

The method of correlation functions is a fundamental tool for solving problems in mathematical statistical physics. It is used to prove the existence of a Gibbs random field with a given potential and to establish its various properties. Due to this, the problem of extending the method of correlation functions to broader classes of physical systems is very relevant. In our previous papers, the method of correlation functions was generalized in two directions: first, by considering spin systems, and second, by applying the concept of a transition energy field. The present paper continues the study of generalized correlation functions. Namely, we prove the group property of correlation functions, which represents a certain type of decay of dependencies between the components of the system.