Abstract
We consider the multicomponent Widom–Rowlison with Metropolis dynamics, which describes the evolution of a particle system where M different types of particles interact subject to certain hard-core constraints. Focusing on the scenario where the spatial structure is modeled by finite square lattices, we study the asymptotic behavior of this interacting particle system in the low-temperature regime, analyzing the tunneling times between its M maximum-occupancy configurations, and the mixing time of the corresponding Markov chain. In particular, we develop a novel combinatorial method that, exploiting geometrical properties of the Widom–Rowlinson configurations on finite square lattices, leads to the identification of the timescale at which transitions between maximum-occupancy configurations occur and shows how this depends on the chosen boundary conditions and the square lattice dimensions.
Original language | English |
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Pages (from-to) | 1-37 |
Number of pages | 37 |
Journal | Journal of Statistical Physics |
Volume | 171 |
Issue number | 1 |
Early online date | 3 Mar 2018 |
DOIs | |
Publication status | Published - Apr 2018 |
Keywords
- Low-temperature regime
- Metropolis Markov chains
- Mixing times
- Pathwise approach
- Tunneling times
- Widom–Rowlinson model