Thermodynamic supercriticality and complex phase diagram for charged Gauss-Bonnet AdS black holes

Abstract

Lee-Yang zero theory plays a crucial role in phase transition theory and is widely employed in the critical behavior of statistical thermodynamics. The supercritical regime of black hole thermodynamics remains a relatively unexplored area, and recent applications of this theory to charged anti-de Sitter (AdS) black holes have initiated probes into this regime, revealing a simple structure partitioned by a single Widom line. In this paper, we apply Lee-Yang theory to charged Gauss-Bonnet AdS black holes, which feature complex phase diagrams (e.g., triple points), to determine how such structures are reflected in the supercritical regime. Notably, we observe a key dimensional difference in that the five-dimensional (5d) system, which lacks a triple point, confirms the known single Widom line structure, while the six-dimensional (6d) system, which admits a triple point, generates two distinct Widom lines. These lines partition the supercritical domain into three sectors (small-, intermediate-, and large- black hole-like phases), corresponding to the three phases coexisting at the triple point. Our results reveal a direct correspondence between the number of coexisting phases at a triple point and the number of distinct supercritical sectors separated by Widom lines.