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

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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.

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Acknowledgements

The author is supported by NWO Grants 639.033.413 and 680.50.1529. The author is grateful to F.R. Nardi, S.C. Borst, and J.S.H. van Leeuwaarden for the precious feedback and helpful discussions related to this work.

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  1. California Institute of Technology, 1200 E California Blvd, Pasadena, CA, 91125, USA

    Alessandro Zocca

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  1. Alessandro Zocca
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Zocca, A. Low-Temperature Behavior of the Multicomponent Widom–Rowlison Model on Finite Square Lattices. J Stat Phys 171, 1–37 (2018). https://doi.org/10.1007/s10955-018-1961-9

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