Supercritical-subcritical correspondence, asymmetric effects and antisymmetric corrections near a critical point

Abstract

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 ($L^\pm$ 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.