Temperature-driven transition of the eight-state Potts model on the quasiperiodic octagonal tiling

Abstract

Attention is focussed on a certain class of crystalline structures wherein the atomic arrangements can be described in terms of periodic arrangements of tiles of two different types—squares and rhombi. Such structures can be regarded as rather simple (unmodulated) approximants of various two-dimensional quasiperiodic structures. Some of the metallic phases which belong to this class are the beta-Mn and the sigma phases which are so related to the octagonal and the dodecagonal quasicrystals respectively, as also certain AlTi intermetallic phases which are derivatives of a quasiperiodic superlattice structure. It is well established that some of these phases can transform into their quasiperiodic counterparts in a continuous manner. Application of the method of projection from higher dimensions to such continuous transformations shows that the transformation to quasiperiodicity initiates through the formation of faults (antiphase boundaries in the case of superlattice structures) in the unmodulated structures.