Low-Temperature Behavior of the Multicomponent Widom–Rowlison Model on Finite Square Lattices

Alessandro Zocca*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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 languageEnglish
Pages (from-to)1-37
Number of pages37
JournalJournal of Statistical Physics
Volume171
Issue number1
Early online date3 Mar 2018
DOIs
Publication statusPublished - Apr 2018

Keywords

  • Low-temperature regime
  • Metropolis Markov chains
  • Mixing times
  • Pathwise approach
  • Tunneling times
  • Widom–Rowlinson model

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