STRUCTURE OF THE PERTURBATION EXPANSION IN A SIMPLE QUENCHED SYSTEM

We investigate the nature of the perturbation expansion of the free en ergy iii 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 e xistence of Griffiths-like singularities. The implications of this res ult for more realistic systems are discussed.