Can correlation effects in a fluid confined in big but finite compartments linked by small openings, such as shallow channels, occur over distances much larger than the bulk correlation length? Recently, Gasparini and co-workers have demonstrated such rather striking ``action-at-a-distance'' effects in a two-dimensional array of microscopic boxes filled with superfluid 4He and linked by either channels or a uniform film. The measurements of several responses show that under certain conditions these boxes can be strongly coupled to the neighboring ones. What seems to be crucial in this work is the size of boxes and connectors and the vicinity of the critical point. It has been suggested that action-at-a-distance effects might be a more general feature of systems with phase transitions than is usually supposed, a view which we confirmed for uniaxial classical ferromagnets and their analogs (simple fluids or binary mixtures in the lattice gas approximation, all belonging to the Ising model universality class of critical phenomena).