### 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 |
---|---|

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