ar X iv : c on d - m at / 9 70 61 16 v 1 1 2 Ju n 19 97 RANDOM TILING TRANSITION IN THREE DIMENSIONS

Three-dimensional icosahedral random tilings are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasi-lattice points in orthogonal space. The specific heat shows a pronounced Schottky type anomaly, but it does not diverge with sample size. The flip susceptibility as defined by Dotera and Steinhardt [Phys. Rev. Lett. 72, 1670 (1994)] diverges and shifts to lower temperatures, thus indicating a transition at T = 0. Contrary to the Kalugin-Katz conjecture, the self-diffusion shows a plateau at intermediate temperature ranges which is explained by energy barriers and a changing number of flipable configurations.