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The Ising model critical point governs the termination of a line of abrupt transitions (e.g., the liquid-gas transition endpoint at high pressure). The universal scaling functions describing the critical behavior in non-zero field have long been a challenge. We show that these scaling functions inherit an essential singularity from the abrupt transition line, associated with the nucleation of droplets in the metastable phase (e.g. the supercooled gas), giving an analytic formula for the singularity and fitting to simulations. This same basic method may be useful in studying other critical points with metastability, such as in glasses and disordered systems.
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