Universal magnetic fluctuations in the two-dimensional XY model

We discuss the probability distribution function for the magnetic order par ameter 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 t hermodynamic 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, usi ng Monte Carlo simulation, that the distribution function, Q(y - [y]), y = (T-1LT/4 pi J) M, is asymmetric universal function. Using a diagramatic tec hnique, we show that the asymmetry comes from three-spin and higher correla tions. If only two-spin correlations are considered, the distribution is Ga ussian. However, as there are contributions from two-spin terms separated b y all distances, the distribution remains broad and is consistent with a di vergent susceptibility. (C) 1998 American Institute of Physics. [S0021-8979 (98)51911-1].