  In a recent paper ["Cluster Model of Decagonal Tilings" (to be published in
Phys. Rev. B)], we have introduced a cluster model for decagonal tilings in two
dimensions. This model is now extended to three dimensions. Two-dimensional
tilings are stacked on top of each other, with a suitable coupling between
adjacent layers. An energy model with interactions leading to a perfect
decagonal quasicrystal at low temperatures is studied by Monte Carlo
simulations. An order parameter is defined, and its dependence on temperature
and system size is investigated. Evidence for a finite-temperature
order-disorder phase transition is presented. The critical exponents of this
transition are determined by finite-size scaling.
