Remarks on the non-compact spin systems

Abstract

For an abstract thermodynamically well behaved local specification describing a lattice spin system with non-compact state space, the author gives a short proof of the independence of the limiting thermodynamics on the typical boundary conditions. This general theorem is then applied to superstable and regular spin systems studied by Lebowitz and Presutti (1980) to simplify and clarify their proof. Another application gives the uniqueness theorem for the limiting Gibbs phase for a class (in general non-superstable) of lattice systems with unbounded spins.