Multicriticality in the Blume-Capel model under a continuous-field probability distribution

The multicritical behavior of the Blume-Capel model with infinite-range interactions is investigated by introducing quenched disorder in the crystal field ${\mathrm{\Delta }}_i$, which is represented by a superposition of two Gaussian distributions with the same width $\sigma$, centered at ${\mathrm{\Delta }}_i=\mathrm{\Delta }$ and ${\mathrm{\Delta }}_i=0$, with probabilities $p$ and $(1-p)$, respectively. A rich variety of phase diagrams is presented, and their distinct topologies are shown for different values of $\sigma$ and $p$. The tricritical behavior is analyzed through the existence of fourth-order critical points as well as how the complexity of the phase diagrams is reduced by the strength of the disorder.