A New Class of Bounds for Correlation Functions in Euclidean Lattice Field Theory and Statistical Mechanics of Spin Systems

Abstract

Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and interesting bounds on correlation functions for general lattice systems. Our method is expected to yield also useful results in Euclidean Field Theory. Furthermore the approach is applicable in situations where other techniques fail, e.g. in the study of phase transitions without breaking of a {\bf continuous} symmetry like $P(ϕ)$-theories with $ϕ(x)$ scalar.