Critical aging of a ferromagnetic system from a completely ordered state

TL;DR

This paper studies the nonequilibrium critical dynamics of ferromagnetic systems starting from an ordered state using the non-linear sigma model and renormalization group analysis, revealing immediate magnetization scaling and aging phenomena.

Contribution

It adapts the non-linear sigma model to analyze aging and critical relaxation in ferromagnets, providing new insights into their nonequilibrium behavior.

Findings

Magnetization exhibits immediate long-time scaling behavior.

Correlation and response functions show aging-related scaling.

Fluctuation-dissipation ratio computed to first order in epsilon.

Abstract

We adapt the non-linear $\sigma$ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in $d=2+\epsilon$ dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behavior almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behavior which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in $\epsilon$ and the relation between transverse and longitudinal fluctuations is discussed.