The zero temperature direction of spontaneous magnetisation of lanthanide ions at a site of cubic symmetry is investigated as a function of the electrostatic and magnetic interactions. For all the values of J between J = 3 and J = 8, two-dimensional diagrams giving the orientation of spontaneous magnetisation are obtai …
Quasicrystals are obtained as the projections of higher dimensional cubic lattices. This paper aims to show that the affine dihedral subgroup Wa(I2(h)) of the affine group Wa(Bn), h = 2n being the Coxeter number, offers a different perspective to -fold symmetric quasicrystallography. The affine group Wa(I2(h)) is const …
We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended Coxeter groups W(A3) and W(B3)=Aut(A3). It is naturally expected that these rank-3 Coxeter-Weyl groups define the point tetrahedral symmetry and the octahedral …
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