Correlation Bound for a One-Dimensional Continuous Long-Range Ising Model

TL;DR

This paper establishes a correlation inequality for a one-dimensional continuum long-range Ising model, providing bounds on magnetic susceptibility with implications for quantum field theory and ground state existence.

Contribution

It introduces a new correlation bound for a continuum long-range Ising model, linking it to quantum field theory applications and ground state proofs.

Findings

Proves a correlation inequality for the continuum long-range Ising model.

Establishes bounds on magnetic susceptibility for small interaction norms.

Demonstrates applications to quantum field theory and spin boson models.

Abstract

We consider a measure given as the continuum limit of a one-dimensional Ising model with long-range translationally invariant interactions. Mathematically, the measure can be described by a self-interacting Poisson driven jump process. We prove a correlation inequality, estimating the magnetic susceptibility of this model, which holds for small $L^1$-norm of the interaction function. The bound on the magnetic susceptibility has applications in quantum field theory and can be used to prove existence of ground states for the spin boson model.