  We consider the hard-core model with Metropolis transition probabilities on
finite grid graphs and investigate the asymptotic behavior of the first hitting
time between its two maximum-occupancy configurations in the low-temperature
regime. In particular, we show how the order-of-magnitude of this first hitting
time depends on the grid sizes and on the boundary conditions by means of a
novel combinatorial method. Our analysis also proves the asymptotic
exponentiality of the scaled hitting time and yields the mixing time of the
process in the low-temperature limit as side-result. In order to derive these
results, we extended the model-independent framework in [27] for first hitting
times to allow for a more general initial state and target subset.
