Structural crossover in a model fluid exhibiting two length scales: repercussions for quasicrystal formation

TL;DR

This study reveals a structural crossover in a 2D model fluid with two length scales, linking it to quasicrystal formation and suggesting a general approach to identify quasicrystals via phase diagram analysis.

Contribution

It demonstrates the connection between structural crossover in fluid correlations and the emergence of quasicrystals, providing a new strategy for their identification in various systems.

Findings

Identified a crossover from one dominant wavelength to another in the radial distribution function.

The wavelength ratio at crossover is approximately 1.932.

Following the crossover line in the phase diagram leads to quasicrystal regions.

Abstract

We investigate the liquid state structure of the two-dimensional (2D) model introduced by Barkan et al. [Phys. Rev. Lett. 113, 098304 (2014)], which exhibits quasicrystalline and other unusual solid phases, focussing on the radial distribution function $g(r)$ and its asymptotic decay $r\to\infty$. For this particular model system, we find that as the density is increased there is a structural crossover from damped oscillatory asymptotic decay with one wavelength to damped oscillatory asymptotic decay with another distinct wavelength. The ratio of these wavelengths is $\approx1.932$. Following the locus in the phase diagram of this structural crossover leads directly to the region where quasicrystals are found. We argue that identifying and following such a crossover line in the phase diagram towards higher densities where the solid phase(s) occur is a good strategy for finding quasicrystals in a wide variety of systems. We also show how the pole analysis of the asymptotic decay of equilibrium fluid correlations is intimately connected with the non-equilibrium growth or decay of small amplitude density fluctuations in a bulk fluid.