  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 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 only observed 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 CP(N-1) field theory.
