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We present what we believe is the first example of a "λ-line" phase transition in black hole thermodynamics. This is a line of (continuous) second order phase transitions which in the case of liquid ^4He marks the onset of superfluidity. The phase transition occurs for a class of asymptotically anti-de Sitter hairy black holes in Lovelock gravity where a real scalar field is conformally coupled to gravity. We discuss the origin of this phase transition and outline the circumstances under which it (or generalizations of it) could occur.
Hennigar et al. (2017) studied this question.