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Sturmian Ground States in Classical Lattice–Gas Models

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Abstract

We construct for the first time examples of non-frustrated, two-body, infinite-range, one-dimensional classical lattice–gas models without periodic ground-state configurations. Ground-state configurations of our models are Sturmian sequences defined by irrational rotations on the circle. We present minimal sets of forbidden patterns which define Sturmian sequences in a unique way. Our interactions assign positive energies to forbidden patterns and are equal to zero otherwise. We illustrate our construction by the well-known example of the Fibonacci sequences.

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Acknowledgements

JM and AvE would like to thank the National Science Centre (Poland) for financial support under Grant No. 2016/22/M/ST1/00536. HK gratefully acknowledges the support of OeAD grant number PL03/2017. JM thanks Karol Penson for introducing to him a wonderful world of the On-Line Encyclopedia of Integer Sequences and Marek Biskup for many helpful discussions.

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Authors and Affiliations

  1. Bernoulli Institute, Nijenborgh 9, Groningen University, 9747AG, Groningen, Netherlands

    Aernout van Enter

  2. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-platz 1, 1090, Vienna, Austria

    Henna Koivusalo

  3. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Jacek Miȩkisz

Authors
  1. Aernout van Enter
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  2. Henna Koivusalo
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  3. Jacek Miȩkisz
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Correspondence to Jacek Miȩkisz.

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Communicated by Bruno Nachtergaele.

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van Enter, A., Koivusalo, H. & Miȩkisz, J. Sturmian Ground States in Classical Lattice–Gas Models. J Stat Phys 178, 832–844 (2020). https://doi.org/10.1007/s10955-019-02464-4

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