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Two numerical strategies based on the Wang-Landau and Lee entropic samplingschemes are implemented to investigate the first-order transition features ofthe 3D bimodal ($\pm h$) random-field Ising model at the strong disorderregime. We consider simple cubic lattices with linear sizes in the range$L=4-32$ and simulate the system for two values of the disorder strength: $h=2$and $h=2.25$. The nature of the transition is elucidated by applying theLee-Kosterlitz free-energy barrier method. Our results indicate that, despitethe strong first-order-like characteristics, the transition remains continuous,in disagreement with the early mean-field theory prediction of a tricriticalpoint at high values of the random-field.

First-order transition features of the 3D bimodal random-field Ising model