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The nonanalyticity and the sign problem in the Z3-symmetric heavy quark modelat low temperature are studied phenomenologically. For the free heavy quarks,the nonanalyticity is analyzed in the relation to the zeros of the grandcanonical partition function. The Z3-symmetric effective Polyakov-line model(EPLM) in strong coupling limit is also considered as an phenomenological modelof Z3-symmetric QCD with large quark mass at low temperature. We examine howthe Z3-symmetric EPLM approaches to the original one in the zero-temperaturelimit. The effects of the Z3-symmetry affect the structure of zeros of themicroscopic probability density function at the nonanalytic point. The averagevalue of the Polyakov line can detect the structure, while the otherthermodynamic quantities are not sensible to the structure in thezero-temperature limit. The effect of the imaginary quark chemical potential isalso discussed. The imaginary part of the quark number density is verysensitive to the symmetry structure at the nonanalytical point. For aparticular value of the imaginary quark number chemical potential, large quarknumber may be induced in the vicinity of the nonanalytical point.

Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses