Criticality in the $N$-flavor London model

We consider the critical properties of $N$-flavor London model in $d=2+1$ dimensions in the phase-only approximation, with {\it no inter-flavor Josephson coupling}. The model applies to superconducting phases of projected metallic states of light atoms and as effective theories for easy-plane quantum antiferromagnets. MC simulations with $N=2$ and unequal bare phase stiffnesses of the components show two anomalies in the specific heat. From the critical exponents $\alpha$ and $\nu$, the mass of the gauge field, and vortex correlation functions, we conclude that these anomalies correspond to an {\it inverted} 3D$xy$ and a 3D$xy$ fixed point. The $N=2$ model with equal phase stiffnesses exhibits one {\it non}-3D$xy$ critical point due to self-duality. For $N=3$ and unequal bare phase stiffnesses we find two neutral 3D$xy$ fixed points and one charged fixed point. The model with the two lower phase stiffnesses equal exhibits one neutral fixed point and one charged fixed point. We find a {\it non}- 3D$xy$ fixed point with $N=3$ and equal bare phase stiffnesses. For the general $N$-flavor model with unequal phase stiffnesses there are $N$ fixed points, namely one inverted 3D$xy$ fixed point, and $N-1$ fixed points in the (neutral) 3D$xy$ universality class. Hence, we find superfluid modes arising from charged condensates.