A self-consistent Ornstein-Zernike approximation for the random field Ising model

We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the rand om field Ising model. Within the replica formalism, we treat the quenched r andom field just as another spin variable, thereby avoiding the usual avera ge over the random field distribution. This allows us to study the influenc e of the distribution on the phase diagram in finite dimensions. The thermo dynamics and the correlation functions are obtained as solutions of a set a coupled partial differential equations with magnetization, temperature, an d disorder strength as independent variables. A preliminary analysis based on high-temperature and lid series expansions shows that the theory can pre dict accurately the dependence of the critical temperature on disorder stre ngth (no sharp transition, however, occurs for d less than or equal to 4). For the bimodal distribution, we find a tricritical point which moves to we aker fields as the dimension is reduced. For the Gaussian distribution, a t ricritical point may appear for d around 4.