The dynamical properties of the finite-size magnetization M in the critical region T less than or equal to T-KTB of the planar rotor model on a L x L square lattice are analyzed by means of microcanonical simulations. The behavior of the q = 0 structure factor at high frequencies is consistent with field-theoretical results, but new additional features occur at lower frequencies. The motion of M determines a region of spectral lines and the presence of a central peak, which we attribute to phase diffusion. Near T-KTB the diffusion constant scales with system size as D similar to L-1.6(3).
