Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics

TL;DR

This paper investigates time reparametrization symmetry in p-spin models, revealing stable fixed points and the spontaneous symmetry breaking in glass states, which may explain dynamical heterogeneity.

Contribution

It analytically explores the existence and nature of time reparametrization symmetry in p-spin models using RG analysis, identifying symmetric and non-symmetric fixed points.

Findings

Identification of three families of stable fixed points.

Symmetric fixed points associated with low temperature dynamics.

Non-symmetric fixed points related to high temperature dynamics.

Abstract

We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.