Emergent symmetry and thermodynamic crossovers for supercritical AdS black holes

Abstract

Ising symmetry typically emerges in the critical domain between liquid-gas phases. Universality of this property imposes strong constraints on the behavior of thermodynamic crossovers for supercritical fluids. In this work, we develop a novel approach to investigate the crossover lines for supercritical AdS black holes using Lee-Yang phase transition theory. We analytically continue Lee-Yang zeros into the complex plane within the supercritical region by keeping a modular pressure real. Consequently, we obtain a pair of complex crossover lines, which exhibit universal scalings and manifest the emergent Ising symmetry in the complex phase space. The real crossover lines are defined by projecting the complex crossovers onto the real phase space. As a result, the phase diagram above the critical point is divided into three distinct regimes: liquid-like, indistinguishable and gas-like states, in sharp contrast to scenarios featuring only a single crossover line.