  We construct general models for holographic superconductivity parametrized by
three couplings which are functions of a real scalar field and show that under
general assumptions they describe superconducting phase transitions. While some
features are universal and model independent, important aspects of the quantum
critical behavior strongly depend on the choice of couplings, such as the order
of the phase transition and critical exponents of second-order phase
transitions. In particular, we study a one-parameter model where the phase
transition changes from second to first order above some critical value of the
parameter and a model with tunable critical exponents.
