Mean-field theory of Archimedean and quasicrystalline tilings

A simple Landau theory of three-component alloy systems under incompressible condition is investigated, which appears to give regions of the phase diagram in which Archimedean tiling phases are stable in two dimensions. Moreover, we find regions where dodecagonal and decagonal quasicrystals appear to be stable. The Alexander-MacTague and Mermin-Troian theories of weak crystallization are revisited.