  Using an effective-field-theory (nonlinear sigma model) description of
interacting electrons in a disordered metal ring enclosing magnetic flux, we
calculate the moments of the persistent current distribution, in terms of
interacting Goldstone modes (diffusons and cooperons). At the lowest or
Gaussian order we reproduce well-known results for the average current and its
variance that were originally obtained using diagrammatic perturbation theory.
At this level of approximation the current distribution can be shown to be
strictly Gaussian. The nonlinear sigma model provides a systematic way of
calculating higher-order contributions to the current moments. An explicit
calculation for the average current of the first term beyond Gaussian order
shows that it is small compared to the Gaussian result; an order-of-magnitude
estimation indicates that the same is true for all higher-order contributions
to the average current and its variance. We therefore conclude that the
experimentally observed magnitude of persistent currents cannot be explained in
terms of interacting diffusons and cooperons.
