Stability of the decagonal quasicrystal in the Lennard-Jones-Gauss system

Although quasicrystals have been studied for 25 years, there are many open questions concerning their stability: What is the role of phason fluctuations? Do quasicrystals transform into periodic crystals at low temperature? If yes, by what mechanisms? We address these questions here for a simple two-dimensional model system, a monatomic decagonal quasicrystal, which is stabilized by the Lennard-Jones-Gauss potential in thermodynamic equilibrium. It is known to transform to the approximant Xi, when cooled below a critical temperature. We show that the decagonal phase is an entropically stabilized random tiling. By determining the average particle energy for a series of approximants, it is found that the approximant Xi is the one with lowest potential energy.