Fluctuations and effective temperatures in coarsening

TL;DR

This paper investigates the fluctuations of response and correlation functions in coarsening ferromagnetic systems at criticality and low temperature, revealing universal scaling behaviors and implications for effective temperatures.

Contribution

It introduces a restricted average of response functions conditioned on correlations, demonstrating universal scaling and insights into time-reparametrization invariance in coarsening systems.

Findings

Restricted average of response obeys a scaling form.

Universal value of the effective temperature slope $X_0$.

Supports the non-realization of time-reparametrization invariance in coarsening.

Abstract

We study dynamic fluctuations in non-disordered finite dimensional ferromagnetic systems quenched to the critical point and the low-temperature phase. We investigate the fluctuations of two two-time quantities, called $\chi$ and $C$, the averages of which %$<\chi>$, $<C>$ yield the self linear response and correlation function. We introduce a restricted average of the $\chi$'s, summing over all configurations with a given value of $C$. We find that the restricted average $<\chi >_C$ obeys a scaling form, and that the slope of the scaling function approaches the universal value $X_\infty $ of the limiting effective temperature in the long-time limit and for $C\to 0$. Our results tend to confirm the expectation that time-reparametrization invariance is not realized in coarsening systems at criticality. Finally, we discuss possible experimental tests of our proposal.