Time-reparametrization invariances, multithermalization and the Parisi scheme

TL;DR

This paper explores how time-reparametrization invariances underpin the Parisi scheme in spin glasses, linking equilibrium states, multithermalization, and slow dynamics through a unified theoretical framework.

Contribution

It demonstrates that time-reparametrization invariances are fundamental to the Parisi scheme and multithermalization in spin glasses, providing a new perspective on their interconnectedness.

Findings

Time-reparametrization invariances are essential for the Parisi scheme.

Multithermalization implies the existence of these invariances.

Systems can reorganize their timescales to match temperatures through these invariances.

Abstract

The Parisi scheme for equilibrium and the corresponding slow dynamics with multithermalization - same temperature common to all observables, different temperatures only possible at widely separated timescales -- imply one another. Consistency requires that two systems brought into infinitesimal coupling be able to rearrange their timescales in order that all their temperatures match: this time reorganisation is only possible because the systems have a set of time-reparametrization invariances, that are thus seen to be an essential component of the scenario.