Correlations in the low-temperature phase of the two-dimensional XY model

Details Correlations in the low-temperature phase of the two-dimensional XY model Correlations in the low-temperature phase of the two-dimensional XY model

2002-08-27

arxiv.org/abs/cond-mat/0208521v1

Europhys. Lett. 60, 539-545 (2002)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 2 eps figures

Scientific paper

10.1209/epl/i2002-00252-0

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 eta_sigma(T) of the order parameter correlation function at any temperature in the critical phase of the model. The temperature behaviour of eta_sigma(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.

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