Using approximate renormalization group methods, the authors map phase diagrams of Z3 spin and gauge models and find that only chiral spin models and their duals show an infinite Devil's flower family of inhomogeneous phases, while different RG schemes disagree on the number of phases.
The sign problem and Abelian lattice duality
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abstract
For a large class of Abelian lattice models with sign problems, including the case of non-zero chemical potential, duality maps models with complex actions into dual models with real actions. For extended regions of parameter space, calculable for each model, duality resolves the sign problem for both analytic methods and computer simulations. Explicit duality relations are given for models for spin and gauge models based on Z(N) and U(1) symmetry groups. The dual forms are generalizations of the Z(N) chiral clock model and the lattice Frenkel-Kontorova model, respectively. From these equivalences, rich sets of spatially-modulated phases are found in the strong-coupling region of the original models.
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Exotic phases in finite-density $\mathbb{Z}_3$ theories
Using approximate renormalization group methods, the authors map phase diagrams of Z3 spin and gauge models and find that only chiral spin models and their duals show an infinite Devil's flower family of inhomogeneous phases, while different RG schemes disagree on the number of phases.