Linear response approximation in effective field theory for the calculation of elastically mediated interactions in one dimension.

The linear response approximation, used within effective field theory to calculate mediated interactions between inclusions, is studied for an exactly solvable one-dimensional model. We show that it works poorly in the case of inclusions imposing absolute deformations to the field, while it works well for massless theories in the case of inclusions imposing relative deformations to the field.