  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.
