Structure factors at and near weak-to-strong pairing quantum Hall phase transitions

We consider a fractional quantum Hall phase transition from a $p$-wave weak-pairing phase to a $p$-wave strong-pairing phase of composite fermions. A candidate for such a phase transition is the transition between the Halperin 331 state to the Moore-Read state in a bilayer quantum Hall system. Using an effective field theory approach, we derive the long-wavelength behavior of the structure factor at and near such phase transitions.