  We calculate the probability density function for the order parameter
fluctuations in the low temperature phase of the 2D-XY model of magnetism near
the line of critical points. A finite correlation length, \xi, is introduced
with a small magnetic field, h, and an accurate expression for \xi(h) is
developed by treating non-linear contributions to the field energy using a
Hartree approximation. We find analytically a series of universal non-Gaussian
distributions with a finite size scaling form and present a Gumbel-like
function that gives the PDF to an excellent approximation. We propose the
Gumbel exponent, a(h), as an indirect measure of the length scale of
correlations in a wide range of complex systems.
