Incommensurate phases in the two-dimensional XY model with Dzyaloshinskii-Moriya interactions

The two-dimensional XY model with Dzyaloshinskii-Moriya interaction has been studied through extensive Monte Carlo simulations. A hybrid algorithm consisting of single-spin Metropolis and Swendsen-Wang clusterspin updates has been employed. Single histogram techniques have been used to obtain the thermodynamic variables of interest and finite-size-scaling analysis has led to the phase transition behavior in the thermodynamic limit. Fluctuating boundary conditions have been utilized in order to match the incommensurability between the spin structures and the finite lattice sizes due to the Dzyaloshinskii-Moriya interaction. The effects of the fluctuating boundary conditions have been analyzed in detail in both commensurate and incommensurate cases. The Berezinskii-Kosterlitz-Thouless transition temperature has been obtained as a function of the Dzyaloshinskii-Moriya interaction and the results are in excellent agreement with the exact equation for the transition line. The spin-spin correlation function critical exponent has been computed as a function of the Dzyaloshinskii-Moriya interaction and temperature. In the incommensurate cases, optimal sizes for the finite lattices and the distribution of the boundary shift angle have been extracted. Analysis of the low temperature configurations and the corresponding vortex-antivortex pairs have also been addressed in some regions of the phase diagram.