Time reparametrization symmetry in spin glass models

TL;DR

This paper investigates the long-time aging dynamics of spin-glass models, revealing a time reparametrization symmetry at the fixed point and its implications for fluctuations and Goldstone modes.

Contribution

It introduces a renormalization group approach to analyze time reparametrization symmetry in spin glasses, identifying a fixed point and its broken symmetry leading to Goldstone modes.

Findings

RG flow converges to an exact fixed point

Fixed point exhibits invariance under time reparametrizations

Broken symmetry results in Goldstone modes influencing fluctuations

Abstract

We study the long-time aging dynamics of spin-glass models with two-spin interactions by performing a Renormalization Group transformation on the time variable in the non-equilibrium dynamical generating functional. We obtain the RG equations and find that the flow converges to an exact fixed point. We show that this fixed point is invariant under reparametrizations of the time variable. This continuous symmetry is broken, as evidenced by the fact that the observed correlations and responses are not invariant under it. We argue that this gives rise to the presence of Goldstone modes, and that those Goldstone modes shape the behavior of fluctuations in the nonequilibrium dynamics.