Supercritical-Subcritical Correspondence, Asymmetric Effects, and Antisymmetric Corrections Near a Critical Point

The second-order phase transitions in the Ising model and liquid-gas systems share a universality class and critical exponents, despite the absence of Z_{2} symmetry in the liquid-gas Hamiltonian. This discrepancy highlights a central puzzle in critical phenomena: what is the influence of asymmetry on scaling laws? For over a century, this question has been explored through examining violations of the empirical "rectilinear diameter law" for the subcritical coexistence curve, where asymmetry could generate singular corrections. Here, we extend this investigation to the supercritical regime. We propose a supercritical-subcritical correspondence, drawing a formal analogy between the subcritical coexistence curve and recently defined supercritical boundary lines (L^{±} lines). Our theory predicts that the linear mixing of physical fields-a hallmark of asymmetric systems-produces universal scaling corrections, with antisymmetric coefficients, in these supercritical loci. We verify these predictions using liquid-gas data from the NIST database and a model liquid-liquid transition. Furthermore, we demonstrate that the same asymmetric scaling framework governs the behavior of higher-order cumulants in the order parameter distribution.