Relaxation processes in a system with logarithmic growth

TL;DR

This paper investigates relaxation and aging in driven diffusive ABC models, revealing logarithmic domain growth, dynamical scaling, and complex finite-time effects through analysis of correlation functions.

Contribution

It provides a detailed analysis of coarsening and aging in ABC models, highlighting the logarithmic growth and dynamical scaling in driven diffusive systems.

Findings

Logarithmic growth of ordered domains over time

Dynamical scaling observed in asymptotic regime

Finite-time and finite-size effects are significant in early and intermediate regimes

Abstract

We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time limit by a logarithmic growth of ordered domains that take the form of stripes. From the time-dependent length, derived from the equal-time spatial correlator, and from the mean displacement of individual particles different regimes in the formation and growth of these domains can be identified. Analysis of two-times correlation and response functions reveals dynamical scaling in the asymptotic logarithmic growth regime as well as complicated finite-time and finite-size effects in the early and intermediate time regimes.