Universal magnetic fluctuations in the two-dimensional XY model

We discuss the probability distribution function for the magnetic order parameter M, in the low temperature phase of the two-dimensional XY model. In this phase the system is critical over the whole range of temperature. The thermally averaged value of the order parameter [M], which is zero in the thermodynamic limit, has abnormally large finite size corrections. An exact result, within a spin wave calculation gives [M] = (1/2N)(T/8 pi J), where J is the magnetic exchange constant and N the number of spins. We show, using Monte Carlo simulation, that the distribution function, Q(y - [y]), y = (T-1LT/4 pi J) M, is asymmetric universal function. Using a diagramatic technique, we show that the asymmetry comes from three-spin and higher correlations. If only two-spin correlations are considered, the distribution is Gaussian. However, as there are contributions from two-spin terms separated by all distances, the distribution remains broad and is consistent with a divergent susceptibility. (C) 1998 American Institute of Physics. [S0021-8979(98)51911-1].