Metastability of Glauber dynamics with inhomogeneous coupling disorder

Anton Bovier, Frank den Hollander, Saeda Marello, Elena Pulvirenti, Martin Slowik

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates of metastability in large volumes at fixed temperatures when these systems evolve according to a Glauber dynamics, i.e. where spins flip with Metropolis transition probabilities at inverse temperature β. We identify conditions ensuring that with high probability the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. This work provides an extension of the results known for the Ising model on the Erdős–Rényi random graph. The proofs use the potential-theoretic approach to metastability in combination with concentration inequalities.

Original languageEnglish
Pages (from-to)1249-1273
Number of pages25
JournalAlea (Rio de Janeiro)
Volume21
Issue number2
DOIs
Publication statusPublished - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Disorder
  • Glauber dynamics
  • metastability
  • random graphs
  • spin systems

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