RPA approach to disorder points

Following Stephenson (1969-70), the authors consider d-dimensional magnetic systems with competing interactions in (d-m) directions. The ground state is assumed to be ferromagnetic. These systems may exhibit, above the critical temperature, disorder points of the first or second kind that they study in the framework of a simple random phase approximation. For disorder points of the first kind, they find that the correlation functions are anisotropic if m is odd; they are simply m-dimensional for disorder points of the second kind. Applying an extra parameter (concentration, pressure, . . .) allows one to consider how a disorder line intersects a critical line; in their model, their happens at a Lifshitz point for disorder lines of the first kind, or at a special point (displaying m-dimensional critical behaviour) for disorder lines of the second kind. Their analysis also suggests the possibility of a disorder point below the critical temperature. Experiments are briefly considered.