Structure of the perturbation expansion in a simple quenched system

We investigate the nature of the perturbation expansion of the free energy in one of the simplest models of a system with quenched disorder: a randomly diluted magnet in zero dimensions. We show that the fact that the series is non-Borel-summable is a direct consequence of the existence of Griffiths-like singularities. The implications of this result for more realistic systems are discussed. © 1994 The American Physical Society.