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

Jacopo Rocchi, David Saad, Chi Ho Yeung

Research output: Contribution to journalArticle

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. 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.

Original languageEnglish
Article number062154
JournalPhysical Review E
Volume97
Issue number6
DOIs
Publication statusPublished - 29 Jun 2018

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Spin Dynamics
spin dynamics
Random Graphs
Spin Glass
Local Field
Regular Graph
spin glass
Message-passing Algorithms
Sparse Graphs
Spin Models
Glass Transition
Snapshot
Flip
Erdös
messages
emerging
Fluctuations
topology
Topology
Imply

Bibliographical note

©2018 American Physical Society

Cite this

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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. 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.",
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Slow spin dynamics and self-sustained clusters in sparsely connected systems. / Rocchi, Jacopo; Saad, David; Yeung, Chi Ho.

In: Physical Review E, Vol. 97, No. 6, 062154, 29.06.2018.

Research output: Contribution to journalArticle

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