https://doi.org/10.1140/epjc/s10052-026-15792-z
Regular Article - Theoretical Physics
Complex plane phase diagram and Widom line for the Born–Infeld black holes with reentrant phase transition
1
School of Physics, Northwest University, 710127, Xi’an, China
2
Peng Huanwu Center for Fundamental Theory, 710127, Xi’an, China
3
Shaanxi Key Laboratory for Theoretical Physics Frontiers, 710127, Xi’an, China
4
Fundamental Discipline Research Center for Quantum Science and Technology of Shaanxi Province, Xi’an, China
a
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Received:
3
March
2026
Accepted:
1
May
2026
Published online:
16
May
2026
Abstract
The Lee–Yang phase transition theory applied in the anti-de Sitter (AdS) black hole has inspired the exploration of complex phase diagram and supercritical phenomena in black hole thermodynamics. In this study, we extend the approach to the four dimensional Born–Infeld AdS black hole. This system exhibits a rich phase structure, including reentrant phase transitions, due to the modulation of the Born–Infeld nonlinear parameter. Through the Lee–Yang zeros, we obtained the complex phase diagram of the Born–Infeld AdS black hole and derived the supercritical crossover line – Widom line, which strictly originates from the first-order stable critical point. The results indicate that Born–Infeld nonlinear effects significantly alter the types and characteristics of phase transition in critical region, while do not disrupt the uniqueness of the Widom line in supercritical region. Our study uncovers a universal simplified feature of the thermodynamic behavior of nonlinear gravitational systems in supercritical region. It also deepens our understanding of the fundamental connection between critical phenomena and continuous phase transitions in the extended phase space of black holes.
© The Author(s) 2026
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