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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
R. M. Robinson, Undecidability and nonperiodicity for tilings of the plane, Invent. Math. ,12, 177 (1971).
B. Grünbaum and G. C. Shephard, “Tilings and Patterns”, Freeman, New York (1986).
J. Miejusz and C. Radiri, The unstable chemical structure of quasicrystalline alloys, Phys. Letts. ,119A, 133 (1986).
J. Miekisz, Stable quasicrystalline ground states, preprint.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Miękisz, J. (1994). Stabilities and Instabilities in Classical Lattice Gas Models without Periodic Ground States. In: Fannes, M., Maes, C., Verbeure, A. (eds) On Three Levels. NATO ASI Series, vol 324. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2460-1_16
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2460-1_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6047-6
Online ISBN: 978-1-4615-2460-1
eBook Packages: Springer Book Archive