Tunneling of the hard‐core model on finite triangular lattices. Issue 1 (15th September 2018)

• Record Type: Journal Article
• Authors: Zocca, Alessandro
• Is Part Of: Random structures & algorithms. Volume 55:Issue 1(2019)
• Page Start: 215
• Page End: 246
• Publication Date: 2018-09-15
• Subjects: finite triangular lattice -- hard‐core model -- Metropolis dynamics -- mixing time -- tunneling time; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20795
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : 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.