  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.
