Tunneling of the hard-core model on finite triangular lattices

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We consider the hard-core model on finite triangular lattices with Metropolis dynamics. Under suitable conditions on the triangular lattice sizes, this interacting particle system has 3 maximum-occupancy configurations and we investigate its high-fugacity behavior by studying tunneling times, that is, the first hitting times between these maximum-occupancy configurations, and the mixing time. The proof method relies on the analysis of the corresponding state space using geometrical and combinatorial properties of the hard-core configurations on finite triangular lattices, in combination with known results for first hitting times of Metropolis Markov chains in the equivalent zero-temperature limit. In particular, we show how the order of magnitude of the expected tunneling times depends on the triangular lattice sizes in the low-temperature regime and prove the asymptotic exponentiality of the rescaled tunneling time leveraging the intrinsic symmetry of the state space.

Original languageEnglish
Pages (from-to)215-246
Number of pages32
JournalRandom Structures and Algorithms
Volume55
Issue number1
DOIs
Publication statusPublished - Aug 2019
Externally publishedYes

Funding

The author has been supported by NWO grants 639.033.413 and 680.50.1529 and is grateful to F.R. Nardi, S.C. Borst, and J.S.H. van Leeuwaarden for the precious feedback on this work.

FundersFunder number
S.C.
Nederlandse Organisatie voor Wetenschappelijk Onderzoek680.50.1529, 639.033.413
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

    Keywords

    • Metropolis dynamics
    • finite triangular lattice
    • hard-core model
    • mixing time
    • tunneling time

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