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Finite-Temperature Order-Disorder Phase Transition in a Cluster Model of Decagonal Tilings

Michael Reichert·Franz Gähler
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Abstract

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.

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Michael Reichert, Franz Gähler. 2003-10-22. Finite-Temperature Order-Disorder Phase Transition in a Cluster Model of Decagonal Tilings. https://arxiv.org/abs/cond-mat/0302074

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