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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 $Δ_{i}$, which is represented by a superposition of two Gaussian distributions with the same width $σ$, centered at $Δ_{i} = Δ$ and $Δ_{i} = 0$, 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 $σ$ 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.