Abstract
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 Manzo et al. (J Stat Phys 115(1/2):591–642, 2004) for first hitting times to allow for a more general initial state and target subset.
| Original language | English |
|---|---|
| Pages (from-to) | 522-576 |
| Number of pages | 55 |
| Journal | Journal of Statistical Physics |
| Volume | 162 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Jan 2016 |
| Externally published | Yes |
Funding
A.??Zocca wishes to thank J. Sohier for the helpful discussions. F.??R.??Nardi, A.??Zocca and S.??C.??Borst wish to thank J.??S.??H.??van Leeuwaarden for the helpful discussions and suggestions at the early stages of the work. This work was financially supported by The Netherlands Organization for Scientific Research (NWO) through the TOP-GO Grant 613.001.012.
Keywords
- Finite grid graphs
- Hard-core model
- Hitting times
- Low temperature
- Metropolis Markov chains
- Mixing times