Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with fixed boundary conditions. Using a conformal mapping, it is very easy to deduce the exponent ησ(T) of the order parameter correlation function at any temperature in the critical phase of the model. The temperature behaviour of ησ(T) is obtained numerically with a good accuracy up to the Kosterlitz-Thouless transition temperature. At very low temperatures, a good agreement is found with Berezinskii's harmonic approximation. Surprisingly, we show some evidence that there are no logarithmic corrections to the behaviour of the order parameter density profile (with symmetry-breaking surface fields) at the Kosterlitz-Thouless transition temperature.
EPL (Europhysics Letters)
- Pub Date:
- November 2002
- Lattice theory and statistics;
- General theory and models of magnetic ordering;
- Condensed Matter - Statistical Mechanics
- 7 pages, 2 eps figures