A generalization of periodic boundary conditions to incorporate fluctuations with wavelength larger than the system size is discussed. These boundary conditions are applied to Monte Carlo calculations on the two-dimensional $\mathrm{XY}$ model. The finite-size effect on the vortex-vortex correlation function, and thereby the dielectric function, is shown to be virtually eliminated. These Monte Carlo data are shown to be in excellent agreement with the Kosterlitz renormalization group equations, and the critical temperature is found to be $T_c=0.8922\mathrm{}\left(2\right)\mathrm{}$.

• Received 31 August 1994

DOI:https://doi.org/10.1103/PhysRevLett.73.3339