Stable quasicrystalline ground states

TL;DR

This paper demonstrates that quasicrystals and similar noncrystalline materials are common in certain phase space regions, providing models with stable quasiperiodic ground states and a criterion for their stability.

Contribution

It introduces classical lattice-gas models with unique, stable quasiperiodic ground states and offers a general stability criterion for nonperiodic ground states.

Findings

Quasicrystals are shown to be generic in some phase space regions.

Constructed models have stable, unique quasiperiodic ground states.

Provided a stability criterion for nonperiodic ground states.

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.