Anomalous long-range correlations at a non-equilibrium phase transition

TL;DR

This paper investigates how long-range correlations in non-equilibrium diffusive systems become anomalous near a second-order phase transition, revealing non-integer power-law decay and singular behavior of cumulants.

Contribution

It demonstrates the anomalous size dependence of correlations and cumulants near a phase transition using the ABC model and Langevin dynamics of Fourier modes.

Findings

Correlation decay becomes a non-integer power of system size L near the transition.

Cumulants of current become singular as the phase transition is approached.

The dynamics of the Fourier mode amplitude explain the anomalous correlations.

Abstract

Non-equilibrium diffusive systems are known to exhibit long-range correlations, which decay like the inverse 1/L of the system size L in one dimension. Here, taking the example of the ABC model, we show that this size dependence becomes anomalous (the decay becomes a non-integer power of L) when the diffusive system approaches a second-order phase transition. This power-law decay as well as the L-dependence of the time-time correlations can be understood in terms of the dynamics of the amplitude of the first Fourier mode of the particle densities. This amplitude evolves according to a Langevin equation in a quartic potential, which was introduced in a previous work to explain the anomalous behavior of the cumulants of the current near this second-order phase transition. Here we also compute some of the cumulants away from the transition and show that they become singular as the transition is approached.