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 language | English |
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Pages (from-to) | 215-246 |
Number of pages | 32 |
Journal | Random Structures and Algorithms |
Volume | 55 |
Issue number | 1 |
DOIs | |
Publication status | Published - Aug 2019 |
Externally published | Yes |
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.
Funders | Funder number |
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S.C. | |
Nederlandse Organisatie voor Wetenschappelijk Onderzoek | 680.50.1529, 639.033.413 |
Nederlandse Organisatie voor Wetenschappelijk Onderzoek |
Keywords
- Metropolis dynamics
- finite triangular lattice
- hard-core model
- mixing time
- tunneling time