Self-sustained clusters as drivers of computational hardness in p-spin models


While macroscopic properties of spin glasses have been thoroughly investigated, their manifestation in the corresponding microscopic configurations is much less understood. Cases where both descriptions have been provided, such as constraint satisfaction problems, are limited to their ground state properties. To identify the emerging microscopic structures with macroscopic phases at different temperatures, we study the p-spin model with p= 3. We investigate the properties of self-sustained clusters, defined as variable sets where in-cluster induced fields dominate over the field induced by out-cluster spins, giving rise to stable configurations with respect to fluctuations. We compute the entropy of self-sustained clusters as a function of temperature and their sizes. In-cluster fields properties and the difference between in-cluster and out-cluster fields support the observation of slow-evolving spins in spin models. The findings are corroborated by observations in finite dimensional lattices at low temperatures.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Mathematics
Uncontrolled Keywords: Optimization problems ,NP-hard problems ,Critical phenomena,Condensed Matter Physics
Publication ISSN: 1550-235X
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2017-07-12
Accepted Date: 2017-06-21
Submitted Date: 2016-11-25
Authors: Rocchi, Jacopo
Saad, David (ORCID Profile 0000-0001-9821-2623)
Yeung, Chi Ho



Version: Accepted Version

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