  It is beyond the present techniques based on perturbation theory to reveal
the nature of phase transitions in strongly interacting field theories.
Recently, the holographic approach has provided us with an effective dual
description, mapping strongly coupled conformal field theories to classical
gravity theories. Resorting to the holographic superconductor model, we propose
a general criterion for the nature of the superconducting phase transition
based on effective interactions between vortices. We find "tricritical" points
in terms of the chemical potential for U(1) charges and an effective
Ginzburg-Landau parameter, where vortices do not interact to separate the
second order (repulsive) from the first order (attractive) transitions. We
interpret the first order transition as the Coleman-Weinberg mechanism, arguing
that it is relevant to superconducting instabilities around quantum
criticality.
