  We give the exact critical frontier of the Potts model on bowtie lattices.
For the case of $q=1$, the critical frontier yields the thresholds of bond
percolation on these lattices, which are exactly consistent with the results
given by Ziff et al [J. Phys. A 39, 15083 (2006)]. For the $q=2$ Potts model on
the bowtie-A lattice, the critical point is in agreement with that of the Ising
model on this lattice, which has been exactly solved. Furthermore, we do
extensive Monte Carlo simulations of Potts model on the bowtie-A lattice with
noninteger $q$. Our numerical results, which are accurate up to 7 significant
digits, are consistent with the theoretical predictions. We also simulate the
site percolation on the bowtie-A lattice, and the threshold is
$s_c=0.5479148(7)$. In the simulations of bond percolation and site
percolation, we find that the shape-dependent properties of the percolation
model on the bowtie-A lattice are somewhat different from those of an isotropic
lattice, which may be caused by the anisotropy of the lattice.
