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There is a study on a square lattice that can predict the existence of multiple phase transitions on a complex plane. We extend the study on the different types of Z Q -symmetric model and different lattices in order to provide more evidence to the existence of multiple phase transitions. We focus on the Z Q -symmetric model with the nearest neighbour interaction on the six spin directions between molecular dipole, i.e. Q = 6 on a triangular lattice. Mainly, the model is defined on the triangular lattice graph with the nearest neighbour interaction. By using the transfer matrix approach, the partition functions are computed for increasing lattice sizes. The roots of polynomial partition function are also computed and plotted in the complex Argand plane. The specific heat equation is used for further comparison. The result supports the existence of the multiple phase transitions by the emergence of the multiple line curves in the locus of zeros distribution for specific type of energy level.

The Z_6-symmetric model partition function on triangular lattice