Monte Carlo Study of the Ferromagnetic Six-State Clock Model on the Triangular Lattice

Abstract

A Monte Carlo study is carried out on the six-state clock model on the triangular lattice. Physical quantities which characterize the Kosterlitz-Thouless (KT) phase transition are calculated. The temperature dependence of the exponent of the spin-pair correlation function, η( T ), in the KT phase is obtained precisely. The exponential divergence of the correlation length, ξ∼ exp ( a t - b ), with the theoretical value, b =0.5, gives a good fit to the data by the present MC simulations by choosing a =1.6∼1.8, η=0.23∼0.25 at the upper critical temperature T U =1.46∼1.49. However, the choice of critical parameters, a ∼3.1, b ∼0.3 and η∼0.28 at T U ∼1.53 gives the most consistent result by a finite-size scaling analysis on several physical quantities. The lower critical temperature, T L , is estimated to be 1.1.