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Abstract

Abstract We investigate the supercritical thermodynamics of Euler–Heisenberg AdS black holes within the framework of Lee–Yang phase transition theory. We show that the system admits two distinct critical points associated with a four-phase thermodynamic structure and identify a degenerate higher-order critical point where the two criticalities merge. Extending the thermodynamic description into the complex domain, we determine the distribution of Lee–Yang singularities and construct the corresponding complex phase diagrams. At the degenerate critical point, we find that a well-defined Widom line emerges despite the absence of a conventional coexistence curve, acting as an effective stability boundary in the supercritical regime. In the two-critical-point regime, the complex phase diagram exhibits two distinct Widom lines, one associated with a coexistence curve and the other arising solely from the complex singularity structure. We further show that the Lee–Yang formalism consistently reproduces the expected phase structure for systems with a single critical point and in the absence of criticality. Our results reveal a rich supercritical phase structure and provide new insights into the origin and physical interpretation of Widom lines.