  We discuss a representation of the Z(3) Gauge-Higgs lattice field theory at
finite density in terms of dual variables, i.e., loops of flux and surfaces. In
the dual representation the complex action problem of the conventional
formulation is resolved and Monte Carlo simulations at arbitrary chemical
potential become possible. A suitable algorithm based on plaquette occupation
numbers and link-fluxes is introduced and we analyze the model at zero
temperature and finite density both in the weak and strong coupling phases. We
show that at zero temperature the model has different first order phase
transitions as a function of the chemical potential both for the weak and
strong coupling phases. The exploratory study demonstrates that alternative
degrees of freedom may successfully be used for Monte Carlo simulations in
several systems with gauge and matter fields.
