Relaxation processes in a system with logarithmic growth

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...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 91; no. 5; p. 052116
Main Authors Brown, Mark O, Galyean, Robert H, Wang, Xiangwen, Pleimling, Michel
Format Journal Article
LanguageEnglish
Published United States 11.05.2015
Subjects
Diffusion
Models, Theoretical
Time Factors
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Summary: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.
ISSN:1550-2376
DOI:10.1103/PhysRevE.91.052116