  We study first- and second-order phase transitions of ferromagnetic lattice
models on scale-free networks, with a degree exponent $\gamma$. Using the
example of the $q$-state Potts model we derive a general self-consistency
relation within the frame of the Weiss molecular-field approximation, which
presumably leads to exact critical singularities. Depending on the value of
$\gamma$, we have found three different regimes of the phase diagram. As a
general trend first-order transitions soften with decreasing $\gamma$ and the
critical singularities at the second-order transitions are $\gamma$-dependent.
