A new multicritical point in anisotropic magnets. III. Ferromagnet in both a random and a uniform field

Abstract

For pt.II see ibid., vol.14, p.3603 (1981). Uniaxially anisotropic magnetic systems with both a random and a uniform magnetic field along the easy axis exhibit rather exotic phase diagrams as function of the anisotropy (a), temperature(T), random field (H0) and uniform field (H). For fixed strong anisotropies, below the tricritical temperature. the coexistence surface (H=0) bifurcates for H not=0 into a pair of symmetrical 'wings' of first-order transitions, bounded by two critical loci which meet at the tricritical point at H=0. On the other side, for fixed weak anisotropies the spin-flop phase spreads out into two symmetrical 'horns' (for H>0 and H<0) containing two tricritical lines which meet at the bicritical point at H=0. At intermediate fixed anisotropies, for large uniform fields, the upper parts of the 'horns' overlap the 'wings'. The global four-dimensional phase diagram has been explicitly constructed using mean-field theory. In the vicinity of the new multicritical point, there is a large variety of critical (random Ising-like, pure xy-like), normal and special bicritical (random Ising-like), tricritical (random Ising-like, pure xy-like), fourth-order (random Ising-like) behaviours, as well as crossovers between these behaviours. The results are applicable to the description of dilute antiferromagnets in a uniform field.