A correlation bound for the one-dimensional heterogeneous Ising model

TL;DR

This paper establishes a new upper bound on correlations in a one-dimensional heterogeneous Ising model, highlighting how coupling strength and external fields influence decay, using random currents in a non-ferromagnetic setting.

Contribution

It introduces a novel correlation bound for heterogeneous 1D Ising models, extending the application of random currents beyond ferromagnetic cases.

Findings

Correlation decay depends on coupling constants and external fields.

The bound applies to non-ferromagnetic Ising models.

The method uses random currents for the first time in this context.

Abstract

We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor coupling constants and the effect of external fields. The proof constitutes an application of random currents to a non-ferromagnetic Ising model.