Stabilities and Instabilities in Classical Lattice Gas Models without Periodic Ground States

  • Jacek Miękisz
Part of the NATO ASI Series book series (NSSB, volume 324)

Abstract

We present a criterion of the stability of nonperiodic ground states. It plays a role of the Peierls condition in models without periodic ground-state configurations. We discuss lattice gas models with stable and unstable nonperiodic ground states. The crystal problem is an attempt to deduce, within statistical mechanics, periodic order in systems of many interacting particles. Our model with a unique stable nonperiodic ground state constitutes a generic counterexample to that problem.

Keywords

CarB 

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References

  1. 1.
    R. M. Robinson, Undecidability and nonperiodicity for tilings of the plane, Invent. Math. ,12, 177 (1971).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    B. Grünbaum and G. C. Shephard, “Tilings and Patterns”, Freeman, New York (1986).Google Scholar
  3. 3.
    J. Miejusz and C. Radiri, The unstable chemical structure of quasicrystalline alloys, Phys. Letts. ,119A, 133 (1986).Google Scholar
  4. 4.
    J. Miekisz, Stable quasicrystalline ground states, preprint.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Jacek Miękisz
    • 1
  1. 1.Instituut voor Theoretische FysicaKatholieke Universiteit LeuvenLeuvenBelgium

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