Slow spin dynamics and self-sustained clusters in sparsely connected systems


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. We then compare the predicted SSC associations with the dynamical properties of spins obtained from numerical simulations and show that SSC association identifies individual slow-evolving spins. Studies of Erdos-Renyi (ER) and random regular (RR) graphs show that spins belonging to SSC are more stable with respect to spin-flip fluctuations, as suggested by the analysis of fully connected models. Further analyses show that SSC association outperforms local fields in predicting the spin dynamics, specifically the group of slow- and fast-evolving spins in RR graphs, for a wide temperature range close to the spin-glass transition. 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. It also implies that single-sample SSC association carries more information than local fields in describing the state of individual spins, when little information can be extracted from the system's topology.

Divisions: College of Engineering & Physical Sciences
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: ©2018 American Physical Society
Publication ISSN: 1550-2376
Last Modified: 29 Nov 2023 11:58
Date Deposited: 16 Jul 2018 11:10
Full Text Link: 10.1103/PhysRevE.97.062154
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://journal ... sRevE.97.062154 (Publisher URL)
PURE Output Type: Article
Published Date: 2018-06-29
Accepted Date: 2018-04-30
Authors: Rocchi, Jacopo
Saad, David
Yeung, Chi Ho



Version: Accepted Version

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