Thermodynamics of hairy black holes in Lovelock gravity

We perform a thorough study of the thermodynamic properties of a class of Lovelock black holes with conformal scalar hair arising from coupling of a real scalar fi eld to the dimensionally extended Euler densities. We study the linearized equations of motion of the theory and describe constraints under which the theory is free from ghosts/tachyons. We then consider, within the context of black hole chemistry, the thermodynamics of the hairy black holes in the Gauss-Bonnet and cubic Lovelock theories. We clarify the connection between isolated critical points and thermodynamic singularities, fi nding a one parameter family of these critical points which occur for well-de fi ned thermodynamic parameters. We also report on a number of novel results, including 'virtual triple points' and the fi rst example of a 'lambda-line' - a line of second order phase transitions - in black hole thermodynamics.