We study the two-dimensional lattice multicomponent Abelian-Higgs model, which is a lattice compact U(1) gauge theory coupled with an $N$-component complex scalar field, characterized by a global $\mathrm{SU}(N)$ symmetry. In agreement with the Mermin-Wagner theorem, the model has only a disordered phase at finite temperature, and a critical behavior is observed only in the zero-temperature limit. The universal features are investigated by numerical analyses of the finite-size scaling behavior in the zero-temperature limit. The results show that the renormalization-group flow of the 2D lattice $N$-component Abelian-Higgs model is asymptotically controlled by the infinite gauge-coupling fixed point, associated with the universality class of the 2D $C{P}^{N-1}$ field theory.

• Received 5 December 2019
• Accepted 30 January 2020

DOI:https://doi.org/10.1103/PhysRevD.101.034511