Transition energy fields in the method of correlation equations

Abstract

In this paper, the well-known method of correlation equations for constructing Gibbs measures is generalized based on the concept of the transition energy field. Using the properties of transition energies, we obtain the system of correlation equations for lattice systems with finite spin space. It is shown that for a sufficiently small value of the one-point transition energies, the corresponding system of correlation functions, considered in infinite space, has a solution which is unique. Finally, the convergence of finite-volume correlation functions to the limiting correlation function is shown.