Stable quasicrystalline ground states
arXiv:cond-mat/9301017 · doi:10.1023/B:JOSS.0000015168.25151.22
Abstract
We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice-gas models with translation-invariant, finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.
14 pages, Latex, 10 figures available upon request, completely revised version
Cited by in corpus (7)
- Undecidability of the Spectral Gap (short version)
- Non-periodic long-range order for fast decaying interactions at positive temperatures
- Undecidability of the Spectral Gap (full version)
- Sturmian ground states in classical lattice-gas models
- Typical ground states for large sets of interactions
- Characterisation of the Set of Ground States of Uniformly Chaotic Finite-Range Lattice Models
- Aperiodicity in equilibrium systems: Between order and disorder