Title: Tunneling of the hard-core model on finite triangular lattices,
Abstract: We consider the hard-core model on finite triangular lattices with Metropolis
dynamics. Under suitable conditions on the triangular lattice dimensions, this
interacting particle system has three maximum-occupancy configurations and we
investigate its high-fugacity behavior by studying tunneling times, i.e., the
first hitting times between 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 dimensions in
the low-temperature regime and prove the asymptotic exponentiality of the
rescaled tunneling time leveraging the intrinsic symmetry of the state space.