Finite-size corrections to scaling of the magnetization distribution in the two-dimensional XY model at zero temperature

The zero-temperature, classical XY model on an L x L square lattice is studied by exploring the distribution Phi(L)(y) of its centered and normalized magnetization y in the large-L limit. An integral representation of the cumulant generating function, known from earlier works, is used for the numerical evaluation of Phi(L) (y), and the limit distribution Phi(L ->infinity)(y) = Phi(0)(y) is obtained with high precision. The two leading finite-size corrections Phi(L)(y) - Phi(0)(y) approximate to a(1)(L) Phi(1)(y)) + a(2)(L) + Phi(2)(y) are also extracted both from numerics and from analytic calculations. We find that the amplitude a(1)(L) scales as ln(L/L-0)/L-2 and the shape correction function Phi(1)(y) can be expressed through the low-order derivatives of the limit distribution, Phi(1)(y) = [y Phi(0)(y) + Phi(0)'(y)]'. Thus, Phi(1)(y) carries the same universal features as the limit distribution and can be used for consistency checks of universality claims based on finite-size systems. The second finite-size correction has an amplitude a(2)(L) proportional to 1/ L-2 and one finds that a(2) Phi(2)(y) << a(1) Phi(1)(y) already for small system size (L > 10). We illustrate the feasibility of observing the calculated finite-size corrections by performing simulations of the XY model at low temperatures, including T = 0.