Certain physical systems are expected classically to exhibit second-order phase transitions but are known to have first-order phase transitions within the renormalization-group approach because no stable fixed point exists. This lack of stable fixed points is caused by fluctuations in the order parameter and depends only upon the symmetry of the system. When a symmetry-breaking field is applied a stable fixed point may emerge and a continuous transition becomes possible. We have studied this crossover from first-order to second-order transitions by three different approaches. Our model has cubic symmetry and the magnetic ground state is similar to that of UO2 and NdSn3. Firstly, Monte Carlo calculations confirm the existence of the crossover to a second-order transition in the symmetry-breaking field. A small field does not destroy the first-order transition, and the crossover therefore occurs at a finite field indicating true tricritical behavior. Secondly, the model has been analyzed using high-temperature series for the ordering susceptibility. For large enough fields the analysis suggests a second-order phase transition at a temperature which is the same as that determined from the Monte Carlo calculations. In this field region the series analysis predicts a bicritical point. For small fields the series behave irregularly, which is considered as an indication of a crossover to first-order transitions. Thirdly, a semiquantitative renormalization-group calculation is presented. This calculation supports and explains the tricritical behavior discovered by the Monte Carlo calculation. Related experimental investigations are suggested on UO2.