Hairy black holes in cubic quasi-topological gravity

We construct a class of five dimensional black hole solutions to cubic quasi-topological gravity with conformal scalar hair and study their thermodynamics. We find these black holes provide the second example of black hole $\lambda$-lines: a line of second order (continuous) phase transitions, akin to the fluid/superfluid transition of $^4$He. Examples of isolated critical points are found for spherical black holes, marking the first in the literature to date. We also find various novel and interesting phase structures, including an isolated critical point occurring in conjunction with a double reentrant phase transition. The AdS vacua of the theory are studied, finding ghost-free configurations where the scalar field takes on a non-zero constant value, in notable contrast to the five dimensional Lovelock case.