Phase transitions in the charged compact abelian lattice Higgs model

Abstract: We consider the (compact) abelian lattice Higgs model with charge ( k \geq 1 ) and show, using charged Wilson~loop observables and charged versions of the Marcu--Fredenhagen ratio, that this model exhibits several distinct phase transitions. In particular, we show that if (k = 2), then the Marcu--Fredenhagen ratio and Wilson~loop observables together can distinguish among three distinct phases of the parameter space, and hence both can be used as order parameters for the model.