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Random systems

 

The best samples of quasicrystals have been measured to have extremely long structural coherence lengths, but they also have the possibility of allowing new types of vibrational excitations : phason modes, in addition to the phonons always present. In an alternative scenario for quasicrystals, it has been proposed that many quasicrystals are intrinsically disordered, and that they belong to an ensemble of random tilings. This should be reflected in a difference in physical properties of the disordered tilings compared to the perfect ly ordered one. We have therefore considered the magnetism of randomized tilings . They are obtained by disordering a perfect Penrose quasicrystal by introducing « phason flips » where a single site is shifted to a new position.

 

A phason flip from the old (blue) to the new (red) position. Bonds are accordingly redefined so that the result is a local shuffling of rhombuses

 

Two local configurations that are not present in the perfect tiling :– the ten-fold star and the vertex of four fat rhombi- that are produced after randomization

 

Staggered magnetization in a randomized tiling showing the greater spatial homogeneity, of the ground state in this case, as well as a lower global average value