New Monte Carlo Simulations to a Generalized XY Model

A new combination Monte Carlo (MC) technique of the classical Metropolis algorithm and the Swendsen--Wang cluster algorithm is proposed. Upon application of the MC technique, the thermodynamic properties of a generalized two-dimensional XY model with chiral Dzyaloshinski--Moriya (DM) interactions are simulated for various DM interactions. The specific heat, order parameter and the integrated correlation time are simulated. We find that there exists a high-temperature Kosterlitz--Thouless-type phase transition related to strong DM spin chiralities. As the DM strength increases the critical temperature of the Kosterlitz--Thouless phase transition increases. It is shown that the combination algorithm is faster than the Metropolis algorithms.