# Slow Spin Dynamics and Self-Sustained Clusters in Sparsely Connected Systems

## TL;DR

This paper introduces a message-passing method to identify slow-evolving spins in sparse spin glasses, linking microscopic structures to dynamics and enabling predictions from static snapshots.

## Contribution

It develops a novel algorithm to detect self-sustained clusters in sparse spin models, connecting static configurations with dynamic behavior.

## Key findings

- SSC association predicts slow-evolving spins
- Method accurately matches dynamical properties from static data
- Potential for broad application in predicting spin dynamics

## Abstract

To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of individual spins to belong to SSC. Results for specific instances, which compare the predicted SSC associations with the dynamical properties of spins obtained from numerical simulations, show that SSC association identifies individual slow-evolving spins. This insight gives rise to a powerful approach for predicting individual spin dynamics from a single snapshot of an equilibrium spin configuration, namely from limited static information, which can be used to devise generic prediction tools applicable to a wide range of areas.