We investigate the subcritical and supercritical behavior of a hard-sphere fluid with attractive interactions described by the Wolf potential, focusing on the role of the interaction range. Coexistence curves are obtained from computer simulations over a wide range of interaction lengths and critical parameters are determined from simultaneous fits of the liquid and vapor branches with the critical exponent $\beta$ treated as a free parameter. As the interaction range decreases, the critical temperature drops rapidly, whereas the critical density displays a nonmonotonic dependence, increasing over most of the range explored before declining mildly at the shortest interaction lengths. The reduced second virial coefficient at criticality, $B_2^{*}\left(T_c\right)$, remains negative over the entire range of interaction lengths and exhibits a nonmonotonic dependence on the inverse-range parameter, suggesting in the short-range regime a finite limiting value distinct from the conventional Noro-Frenkel prediction. In the supercritical region, we analyze parallel critical-isochore (PCI) Widom lines using a previously developed Helmholtz free-energy expression. These lines define a thermodynamic framework that bounds conventional Widom lines associated with extrema of response functions. Their evolution with interaction range reveals a strong asymmetry between the PCI Widom lines branches and characterizes the extension of criticality into the supercritical domain. We additionally examine the Zeno and Boyle ideal lines, which converge in the dilute limit and exhibit a systematic, $\alpha$-dependent curvature away from it.

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• Classical statistical mechanics
• Critical phenomena
• Equations of state
• Phase diagrams