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 random field Ising model. Within the replica formalism, we treat the quenched random field just as another spin variable, thereby avoiding the usual average over the random field distribution. This allows us to study the influence of the distribution on the phase diagram in finite dimensions. The thermodynamics and the correlation functions are obtained as solutions of a set a coupled partial differential equations with magnetization, temperature, and disorder strength as independent variables. A preliminary analysis based on high-temperature and 1/d series expansions shows that the theory can predict accurately the dependence of the critical temperature on disorder strength (no sharp transition, however, occurs for d≤4). For the bimodal distribution, we find a tricritical point which moves to weaker fields as the dimension is reduced. For the Gaussian distribution, a tricritical point may appear for d around 4.