Small-scale structures put on an n-dimensional object embedded in (D+1)-dimensional spacetime modify in general the energy per unit n-volume and tension (or pressure) of the coarse-grained n-dimensional object. We seek fixed points of the renormalization group equations, i.e. equations of states that are independent of the presence of small-scale structures and find that these fixed points exist only for n = 1 case (the string), especially for the Nambu-Goto strings.