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We report a high-precision numerical estimation of the critical exponent$\alpha$ of the specific heat of the random-field Ising model in fourdimensions. Our result $\alpha = 0.12(1)$ indicates a diverging specific-heatbehavior and is consistent with the estimation coming from the modifiedhyperscaling relation using our estimate of $\theta$ via the anomalousdimensions $\eta$ and $\bar{\eta}$. Our analysis benefited form ahigh-statistics zero-temperature numerical simulation of the model for twodistributions of the random fields, namely a Gaussian and Poissoniandistribution, as well as recent advances in finite-size scaling and reweightingmethods for disordered systems. An original estimate of the critical slowingdown exponent $z$ of the maximum-flow algorithm used is also provided.

Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model