Multicomponent compact Abelian-Higgs lattice models

Understand

We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N-component complex field z_x^a of unit length and charge is coupled to compact quantum electrodynamics in the usual Wilson lattice formulation.

• We determine the phase diagram and study the nature of the transition line for N=2 and N=4.
• Two phases are identified, specified by the behavior of the gauge-invariant local composite operator Q_x^{ab} = \bar{z}_x^a z_x^b - \delta^{ab}/N, which plays the role of order parameter.
• In one phase, we have \langle Q_x^{ab}\rangle =0, while in the other Q_x^{ab} condenses.