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

TL;DR

This paper introduces new bounds on correlation functions in lattice spin systems and Euclidean field theory, extending classical statistical mechanics methods to analyze phase transitions without symmetry breaking.

Contribution

It develops a novel approach based on an extended Poisson bracket structure and KMS property, applicable where traditional techniques are ineffective.

Findings

Derived new bounds on correlation functions for lattice systems

Applicable to Euclidean field theory and phase transitions without symmetry breaking

Method extends classical statistical mechanics tools to broader contexts

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 $P(\phi)$-theories with $\phi (x)$ scalar.