Correlation asymptotics for non-translation invariant lattice spin systems

TL;DR

This paper derives asymptotic formulas for Green kernels and two-point correlation functions in non-translation invariant lattice spin systems using advanced analytical methods.

Contribution

It introduces new asymptotic expressions for Green kernels and correlation functions in non-translation invariant lattice models, extending previous results.

Findings

Asymptotic expressions for Green kernels obtained.

Asymptotic formulas for two-point correlation functions derived.

Results apply to certain non-translation invariant lattice models.

Abstract

We obtain asymptotic expressions for the Green kernels of certain non-translation invariant transition matrices using methods of semiclassical and microlocal analysis. Combined with a result by Bach and M{\o}ller this yields asymptotic formulas for the truncated two-point correlation functions of certain non-translation invariant lattice models of real-valued spins.