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