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Lattice field theories with complex actions are not easily studied usingconventional analytic or simulation methods. However, a large class of thesemodels are invariant under CT, where C is charge conjugation and T is timereversal, including models with non-zero chemical potential. For Abelian modelsin this class, lattice duality maps models with complex actions into dualmodels with real actions. For extended regions of parameter space, calculablefor each model, duality resolves the sign problem for both analytic methods andcomputer simulations. Explicit duality relations are given for models for spinand gauge models based on Z(N) and U(1) symmetry groups. The dual forms aregeneralizations of the Z(N) chiral clock model and the latticeFrenkel-Kontorova model, respectively. From these equivalences, rich sets ofspatially-modulated phases are found in the strong-coupling region of theoriginal models.

The Sign Problem, PT Symmetry and Abelian Lattice Duality