Long range correlations and phase transition in non-equilibrium diffusive systems

TL;DR

This paper derives explicit formulas for long-range correlations in non-equilibrium diffusive systems, revealing phase transitions through singularities in two-point correlation functions.

Contribution

It provides explicit expressions for correlations in the ABC model and conditioned diffusive models, highlighting phase transition signatures.

Findings

Correlation functions become singular at phase transition points

Explicit formulas for long-range correlations are derived

Phase transitions are detectable via correlation singularities

Abstract

We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the occurrence of a phase transition as they become singular when the system approaches the transition.