Large Deviations of Correlation Functions in Random Magnets

TL;DR

This paper develops a large deviations theory for spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, revealing how rare, strongly correlated spin pairs influence phase transitions at critical points.

Contribution

It introduces a novel large deviations framework for analyzing correlation functions in disordered magnetic systems at finite and zero temperature.

Findings

Rare events dominate critical behavior at phase transitions.

Number of correlated spin pairs scales linearly with distance at zero temperature critical point.

Correlation functions exhibit non-exponential large deviations at criticality.

Abstract

We present a large deviations theory of the spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, both at finite and zero temperature. Rare events of atypically correlated variables are particularly important at the critical point: the phase transition is driven by few pairs of strongly correlated spins, while the majority remains basically uncorrelated. At the zero temperature critical point the number of spin pairs correlated over a distance L is shown to be no longer exponential, but only linear in the spins separation.