Fluctuation induced first order transitions and symmetry breaking fields

Model Hamiltonians which possess no stable fixed point or which lie outside the domain of attraction of their stable fixed point, are known to yield first order transitions within the renormalization group approach. By applying a symmetry breaking field, g, a continuous transition may be restored. The crossover from first order to continuous transition induced by symmetry breaking fields is analyzed. Two Landau-Ginzburg-Wilson models are considered: (a) the n = 6-component model associated with type-I fcc antiferromagnets (such as UO2), and (b) the n = 4-component model associated with type-II fcc antiferromagnets (such as TbP, TbAs, CeTe and TbSe). The symmetry breaking field corresponds to a magnetic field or a uniaxial stress. The phase diagrams are studied using large g expansions, means field calculations, and renormalization group techniques in d = 4-ε dimensions. It is found that the (g,T) phase diagrams are rather complex exhibiting fourth order critical points, tricritical points and critical end points.