The relation between Parisi scheme and multi-thermalized dynamics in finite dimensions
Disordered Systems and Neural Networks
2022-07-13 v1
Abstract
In this note we summarize the connections between equilibrium and slow out of equilibrium dynamics in finite dimensional glasses, such as we understand them today. If we assume that a finite-dimensional system is stable with respect to a family of weak random perturbations (stochastic stability), then its dynamics have a `Multithermalization' structure if and only if the Boltzmann-Gibbs distribution obeys an Ultrametric Parisi distribution.
Cite
@article{arxiv.2207.05720,
title = {The relation between Parisi scheme and multi-thermalized dynamics in finite dimensions},
author = {Silvio Franz and Jorge Kurchan},
journal= {arXiv preprint arXiv:2207.05720},
year = {2022}
}
Comments
To appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific