Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses

TL;DR

This paper investigates fluctuations in the out-of-equilibrium dynamics of glassy systems, proposing that time-reparametrization invariance explains their scaling behavior, with numerical tests confirming its applicability in spin-glasses but not in ferromagnetic models.

Contribution

It extends theoretical ideas on time-reparametrization invariance to predict scaling of high-order correlations and tests these predictions in different models.

Findings

Scaling properties align with time-reparametrization invariance in spin-glasses.

Different fluctuation behaviors observed between spin-glasses and ferromagnetic models.

Numerical results support the theoretical framework in systems where invariance develops asymptotically.

Abstract

This article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically we deduce the scaling properties of diverse high-order correlation functions. We examine these predictions with numerical tests in a standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system where time-reparametrization invariance is not expected to hold, the 2d ferromagnetic Ising model, both at low temperatures. Our results enlighten a qualitative difference between the fluctuation properties of the two models and show that scaling properties conform to the time-reparametrization invariance scenario in the former but not in the latter.