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arXiv · 1604.02977

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

Takehiro Hirakida·Hiroaki Kouno·Junichi Takahashi·Masanobu Yahiro
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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 $μ-κ$ plane as the number of states increases, where $μ$ $(κ)$ 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 $μ$-dependence with respect to increasing the number of states.

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Takehiro Hirakida, Hiroaki Kouno, Junichi Takahashi, Masanobu Yahiro. 2016-06-14. Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model. https://doi.org/10.1103/physrevd.94.014011

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