Spectral derivation of the ornstein-zernike decay for four-point functions

Abstract

In this note we discuss the relation between the Ornstein-Zernike decay of certain four-point functions ("energyenergy correlations") in lattice spin systems and spectral properties of the transfer matrix, related to the property of two-particle asymptotic completeness in (massive) Euclidean lattice quantum field theories.

Asymptotics of even–even correlations in the Ising model

“…It turned out that Polyakov's predictions were correct. For sufficiently small values of β, this was first proved by Bricmont and Fröhlich [6,7] for dimensions d ≥ 4, and then by Minlos and Zhizhina [29,19] for dimensions 2 and 3; see also [3,4]. Extensions to general even-even correlations, at small values of β, were proved in [29,19,5].…”