Azbel-Hofstadter model on triangular lattice revisited

Details Azbel-Hofstadter model on triangular lattice revisited Azbel-Hofstadter model on triangular lattice revisited

2001-04-12

arxiv.org/abs/cond-mat/0104219v1

Phys. Rev.B 64, 081101 (R) (2001)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

RevTeX, 4 page, no figure

Scientific paper

10.1103/PhysRevB.64.081101

In the present paper, the mean of Lyapunov exponents for the Azbel-Hofstadter model on the triangular lattice is calculated. It is recently proposed that [Phys. Rev. Lett. {\bf 85}, 4920 (2000)], for the case of the square lattice, this quantity can be related to the logarithm of the partition function of the two dimensional Ising model and has a connection to the asymptotic bandwidth. We find that the correspondence of this quantity to the logarithm of the partition function of the two dimensional Ising model is not complete for the triangular lattice. Moreover, the detailed connection between this quantity and the asymptotic bandwidth is not valid. Thus the conclusions for the mean of Lyapunov exponents suggested previously depend on the lattice geometry.

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