Interpretations of heat capacity data fron the random system Fe1-xZnx F2 are presented. The Ginzburg criterion is extended to random-field systems and it is argued that the failure of the supersymmetry formalism prediction of dimensional reduction by two is due to the divergence of thermal fluctuations in fewer than four spatial dimensions. The droplet model for randomfields is studied and a first-order transition is predicted for any infinitesimal randomfield in the neighborhood of the zero-fieldcritical point.