Crossover from fluctuation-driven continuous transitions to first-order transitions

Near a tricritical point of an n-component spin system, fluctuations turn the first-order transition (predicted by the Landau theory) into second order. We show that when this happens, quadratic anisotropies turn the transition first order again. In systems which exhibit fluctuation-driven first-order transitions, increasing anisotropies yield two consecutive tricritical points. These effects are predicted to result from the application of magnetic fields or uniaxial stresses to MnO, BaTiO3, KTaxNb1-xO3 (KTN), TbP, etc.