Detecting Structured Signals in Ising Models

TL;DR

This paper investigates how dependence affects the detection of structured signals in various Ising models, revealing the beneficial role of criticality and providing new insights into correlation behaviors across different regimes.

Contribution

It introduces new methods for analyzing correlation decay and mixing in Ising models, enhancing understanding of signal detection in dependent systems.

Findings

Correlation decay aids signal detection in Ising models

Criticality improves detection of lower signals

Sharp control of mixing and correlations across temperature regimes

Abstract

In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models on lattices, and Mean-Field type Ising Models (Erd\H{o}s-R\'{e}nyi, Random regular, and dense graphs). Our results rely on correlation decay and mixing type behavior for Ising Models, and demonstrate the beneficial behavior of criticality in the detection of strictly lower signals. As a by-product of our proof technique, we develop sharp control on mixing and spin-spin correlation for several Mean-Field type Ising Models in all regimes of temperature -- which might be of independent interest.