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We consider the hard-core model on finite triangular lattices with Metropolisdynamics. Under suitable conditions on the triangular lattice dimensions, thisinteracting particle system has three maximum-occupancy configurations and weinvestigate its high-fugacity behavior by studying tunneling times, i.e., thefirst hitting times between between these maximum-occupancy configurations, andthe mixing time. The proof method relies on the analysis of the correspondingstate space using geometrical and combinatorial properties of the hard-coreconfigurations on finite triangular lattices, in combination with known resultsfor first hitting times of Metropolis Markov chains in the equivalentzero-temperature limit. In particular, we show how the order of magnitude ofthe expected tunneling times depends on the triangular lattice dimensions inthe low-temperature regime and prove the asymptotic exponentiality of therescaled tunneling time leveraging the intrinsic symmetry of the state space.

Tunneling of the hard-core model on finite triangular lattices