Monte Carlo Numerical Study Of Chiral Spin Model

We study the three-state chiral Potts model in two dimensional (rectangular and triangular) and three dimensional (pyrochlore and hyperkagome) lattices using Monte Carlo simulation.The three-state chiral Potts model on rectangular lattices has four phases, paramagnetic, ferromagnetic, modulated and chiral phase, where modulated pha-se is an incommensurate phase. However, there are only three phases, parama-gnetic, ferromagnetic and chiral phase for the three-state chiral Potts model on triangular lattices. For the ground state spin configurations, spins are chiral or-derd along the direction of chiral field in chiral phases in both models.Pyrochlore lattice is a cubic lattice where each unit cell contains four tetr-ahedra. For the three-state chiral Potts model in pyrochlore lattices, no matter how the chiral field is chosen, the surfaces within a unit cell can’t form fully chiral spin configuration simultaneously. Therefore, the ground state is partially chiral ordered when the magnitude of the chiral field is of 0.5<△<1. Hyperk-agome lattice is a cubic lattice where each unit cell contains four triangles. For the three-state chiral Potts model in hyperkagome lattices, one can chose the c-hiral field to be unindirected, so that the spins can be fully chiral. At the gro-und state, the system is partially chiral when the chiral field is of 0.5<△< 1 while is fully chiral when the chiral field is of 1<△< 1.5. Moreover, because of the latice translation symmetry, we find that spins can be spiral ordered (d-ouble or triplespiral) in both lattices.