The zeros distribution of Z5 and Z6-symmetric models on triangular lattice

Abstract

We study the Z_Q-symmetric model with the nearest neighbor interaction between molecular dipole. There were previous study on a square lattice by Martin in 1991 and also Zakaria in 2016 suggesting that the emergence of the linear arcs on the complex-temperature plane can predict the existence of multiple phase transitions. Motivated from their works, we continue to study the model on the triangular lattice specifically on the five spin directions, that is Q=5 and then continue extending our study on Q=6. The aim of this study is to provide more evidence on the existence of multiple phase transitions on the crystal lattice. The model is initially defined on a specific lattice which is the triangular lattice with the nearest neighbor interaction. The partition function is computed for the increasing lattice sizes by using the transfer matrix approach. By applying the Newton-Raphson method, the zeros of the partition function are computed and then plotted in the complex Argand plane for analysis. The number of linear arcs on the graph suggesting the number of phase transition. To support our claim, the specific heat equation is used for further comparison.