Random Tiling Transition in Three Dimensions

TL;DR

This study investigates the phase transition behavior of three-dimensional icosahedral random tilings, revealing a zero-temperature transition and unique diffusion properties, challenging previous conjectures.

Contribution

It introduces a global energy measure and analyzes the transition characteristics, providing new insights into the thermodynamics of 3D random tilings.

Findings

Specific heat exhibits a Schottky anomaly without divergence.

Flip susceptibility diverges and shifts to lower temperatures, indicating a T=0 transition.

Self-diffusion shows a plateau at intermediate temperatures, contrary to prior expectations.

Abstract

Three-dimensional icosahedral random tilings are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice 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.