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

Jacopo Rocchi*, David Saad, Chi Ho Yeung

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Article number024415
    JournalPhysical Review B
    Issue number2
    Publication statusPublished - 12 Jul 2017


    • Optimization problems
    • NP-hard problems
    • Critical phenomena


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