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

Physical Review. E
Jacopo RocchiChi Ho Yeung

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 i...Continue Reading

References

Mar 10, 1986·Physical Review Letters·D J Thouless
Jan 4, 2001·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·F Ricci-Tersenghi, R Zecchina
Jun 15, 2007·Proceedings of the National Academy of Sciences of the United States of America·Florent KrzakałaLenka Zdeborová
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Chi Ho Yeung, David Saad

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Citations

Dec 6, 2018·Physical Review Letters·Yi-Zhi XuDavid Saad

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