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, BaTi${\mathrm{O}}_3$, $\mathrm{K}{\mathrm{Ta}}_x{\mathrm{Nb}}_{1-x}{\mathrm{O}}_3$ (KTN), TbP, etc.