Tunneling of the hard-core model on finite triangular lattices

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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
Issue number1
Publication statusPublished - Aug 2019
Externally publishedYes


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


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