A three-state Ising model properly describing crystal, liquid, and gas phases of a simple substance like argon [Phys. Rev. E 109, 014123 (2024)] is analyzed at a mean-field level in connection with metastable states and spinodal limits. This mainly comprises the stretched liquid and crystal at negative pressure, the superheated liquid and crystal, the supercooled liquid, and the metastable continuations of binodal curves. The model is consistent with available information from experiment and simulation, except for a supercooled liquid spinodal that it predicts. This defect is repaired by devising an enhanced four-state model, with the consequence that spinodal suppression is relevant to the topic of one-component liquid–liquid criticality. The present work on a simple substance thus paves the way to addressing the interplay between the crystal and supercooled liquid phases of water theoretically.

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• Classical statistical mechanics
• Equations of state
• Order parameters
• Phase diagrams
• Phase separation
• Thermodynamics
• Transition temperature