Multi-Higgs U(1) Lattice Gauge Theory in Three Dimensions

We study the three-dimensional compact U(1) lattice gauge theory with $N$ Higgs fields numerically. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. For N=2, the system has a second-order phase transition line ${\tilde{c}}_1(c_2)$ in the $c_2$(gauge coupling)$-c_1$(Higgs coupling) plane, which separates the confinement phase and the Higgs phase. For N=3, the critical line is separated into two parts; one for $c_2\text{alt}2.25$ with first-order transitions, and the other for $c_2\text{agt}2.25$ with second-order transitions.