Finite Size Effects on Spin Glass Dynamics

TL;DR

This paper explores how finite size effects influence the dynamics of spin glasses, affecting scaling behaviors in magnetization decay and susceptibility, and proposes using these effects to determine particle size distributions.

Contribution

It introduces qualitative arguments linking finite size effects to deviations in scaling laws in spin glass dynamics, enabling particle size distribution extraction.

Findings

Deviations from t/{t_w} scaling occur with finite size effects.

Characteristic times for magnetization decay deviate from linearity at higher fields.

Scaling of susceptibility decay changes with magnetic field at large ωt.

Abstract

The recent identification of a time and temperature dependent spin glass correlation length, $\xi({t_w},T)$, has consequences for samples of finite size. Qualitative arguments are given on this basis for departures from t/{t_w} scaling for the time decay of the thermoremanent magnetization, {M_{TRM}}(t,{t_w},T), where t is the measurement time after a ``waiting time'' t_w, and for the imaginary part of the ac susceptibility, ${\chi^{{\prime}{\prime}}}(\omega,t)$. Consistency is obtained for a more rapid decay of $M_{TRM}(t,{t_w},T)$ with increasing t_w when plotted as a function of t/{t_w}, for the deviation of the characteristic time for {M_{TRM}}(t,{t_w},T) from a linear dependence upon H^2 at larger values of H, and for the deviation of the decay of ${\chi^{{\prime}{\prime}}}(\omega,t)$ from $\omega t$ scaling upon a change in magnetic field at large values of $\omega t$. These departures from scaling can, in principle, be used to extract the particle size distribution for a given spin glass sample.