  We study a three dimensional Abelian Higgs model containing singly- and
doubly-charged scalar fields coupled to a compact Abelian gauge field in the
London limit. The model attracts interest because of its relevance to high-Tc
superconductors with charge 1 holon and charge 2 spinon-pair fields. It
contains two types of vortices carrying magnetic flux and one type of
instanton-like monopoles. Using thermodynamic and topological observables we
present the phase diagram in the parameter space of the gauge and holon and
spinon-pair couplings. The Fermi liquid, the spin gap, the superconductor and
the strange metallic phases have been identified in a wide region of
parameters. The model may serve as a toy system modelling non-perturbative
properties of the Yang-Mills theory.
