title: First- and second-order phase transitions in scale-free networks.
abstract: 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.