Azbel-Hofstadter model on the triangular lattice revisited - art. no. 081101

In the present paper, the mean of Lyapunov exponents for the Azbel-Hofstadt er model on the triangular lattice is calculated. It was recently proposed that [Phys. Rev. Lett. 85, 4920 (2000)], for the case of the square lattice , this quantity can be related to the logarithm of the partition function o f the two-dimensional Ising model and has a connection to the asymptotic ba ndwidth. We find that: the correspondence of this quantity to the logarithm of the partition function of the two-dimensional Ising model is not comple te for the triangular lattice. Moreover, the detailed connection between th is quantity and the asymptotic bandwidth is not valid. Thus the conclusions for the mean of Lyapunov exponents suggested previously depend on the latt ice geometry.