  We investigate a holographic superconductor that admits an analytic treatment
near the phase transition. In the dual 3+1 dimensional field theory, the phase
transition occurs when a scalar operator of scaling dimension two gets a vacuum
expectation value. We calculate current-current correlation functions along
with the speed of second sound near the critical temperature. We also make some
remarks about critical exponents. An analytic treatment is possible because an
underlying Heun equation describing the zero mode of the phase transition has a
polynomial solution. Amusingly, the treatment here may generalize for an order
parameter with any integer spin, and we propose a Lagrangian for a spin two
holographic superconductor.
