  Critical Casimir effect appears when critical fluctuations of an order
parameter interact with classical boundaries. We investigate this effect in the
setting of a Landau-Ginzburg model with continuous symmetry in the presence of
quenched disorder. The quenched free energy is written as an asymptotic series
of moments of the models partition function. Our main result is that, in the
presence of a strong disorder, Goldstone modes of the system contribute either
with an attractive or with a repulsive force. This result was obtained using
the distributional zeta-function method without relying on any particular
ansatz in the functional space of the moments of the partition function.
