A new multicritical point in anisotropic magnets: II. Ferromagnetic in a random skew field

The phase diagram of an anisotropic ferromagnetic in a skew random magnetic field is studied as a function of the temperature, anisotropy and two random field components. At fixed high anisotropy, there exists a single ordered phase, bounded by surfaces of second- and first-order transitions separated by a line of tricritical points. As the anisotropy is decreased, the low-temperature tricritical points split into pairs of critical points (inside the ordered phase) and critical end points. The lines of critical points, critical end points and tricritical points meet at a critical point of fourth order. As the anisotropy decreases, this fourth-order critical point moves to lower transverse fields and higher temperatures until it reaches the temperature-longitudinal- field plane exactly at the new multicritical point found in the first paper in this series. For lower anisotropies there is no longer any first-order transition between the ordered and disordered phases. Instead, there exists a spin-flop 'shelf', inside the ordered phase, ending at a bicritical point. In the general four-parameter (temperature, anisotropy, longitudinal random field, transverse random field) space, the new multicritical point occurs where the lines of bicritical points and of fourth-order critical points meet. All of these results have been calculated explicitly using mean-field theory. Due to the random fields, the mean-field predictions for the fourth-order critical points break at 4²/₃ dimensions, and are replaced by renormalisation-group estimates. The results may be observed experimentally in random exchange antiferromagnets with a uniform magnetic field.