  We address the problem of the role of the concept of local rigidity in the
family of sandpile systems. We define rigidity as the ratio between the
critical energy and the amplitude of the external perturbation and we show, in
the framework of the Dynamically Driven Renormalization Group (DDRG), that any
finite value of the rigidity in a generalized sandpile model renormalizes to an
infinite value at the fixed point, i.e. on a large scale. The fixed point value
of the rigidity allows then for a non ambiguous distinction between
sandpile-like systems and diffusive systems. Numerical simulations support our
analytical results.
