Dimensionality Dependence of Aging in Kinetics of Diffusive Phase Separation: Behavior of order-parameter autocorrelation

TL;DR

This study investigates how the aging behavior of autocorrelation during phase separation in binary mixtures depends on spatial dimensionality, using numerical and simulation methods to reveal power-law decay with unexpected exponents.

Contribution

It provides empirical full forms of autocorrelation in 2D and 3D, demonstrating dimensionality effects on aging in phase separation, validated across two different models.

Findings

Autocorrelation exhibits power-law decay with higher-than-expected exponents.

Results are consistent between Cahn-Hilliard and Ising models.

Dimensionality significantly influences aging behavior in phase separation.

Abstract

Behavior of two-time autocorrelation during the phase separation in solid binary mixtures are studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art methods, including the finite-size scaling technique. Full forms of the autocorrelation in space dimensions $2$ and $3$ are obtained empirically. The long time behavior are found to be power-law type, with exponents unexpectedly higher than the ones for the ferromagnetic ordering. Both Chan-Hilliard and Ising models provide results consistent with each other.