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

This paper 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-reparameterization 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-reparameterization 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-reparameterization invariance scenario in the former but not in the latter.