Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model

Abstract

We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models, each with different number of states at each site on a 3-d lattice, by extending the 3-d three-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the $\mu -\kappa$ plane as the number of states increases, where $\mu$ $(\kappa )$ plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $\mu$-dependence with respect to increasing the number of states.

13 pages, 13 figures

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• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
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