Duals of lattice Abelian models with static determinant at finite density

Dual formulations of Abelian U(1) and Z(N) LGT with a static fermion determinant are constructed at finite temperatures non-zero chemical potential. The dual form is valid for broad class lattice gauge actions, arbitrary number flavors in any dimension. distinguished feature the formulation that Boltzmann weight strictly positive. This allows to gain reliable results density via Monte Carlo simulations. As byproduct representation we outline an exact solution partition function (1 + 1)-dimensional theory reveal existence phase oscillating correlations.