  We investigate a novel mechanism for phase transitions that is a distinctive
feature of higher-curvature gravity theories. For definiteness, we bound
ourselves to the case of Lovelock gravities. These theories are known to have
several branches of asymptotically AdS solutions. Here, extending our previous
work, we show that phase transitions among some of these branches are driven by
a thermalon configuration: a bubble separating two regions of different
effective cosmological constants, generically hosting a black hole in the
interior. Above some critical temperature, this thermalon configuration is
preferred with respect to the finite-temperature AdS space, triggering a
sophisticated version of the Hawking-Page transition. After being created, the
unstable bubble configuration can in general dynamically change the asymptotic
cosmological constant. While this phenomenon already occurs in the case of a
gravity action with square curvature terms, we point out that in the case of
Lovelock theory with cubic (and higher) terms new effects appear. For instance,
the theory may admit more than one type of bubble and branches that are in
principle free of pathologies may also decay through the thermalon mechanism.
We also find ranges of the gravitational couplings for which the theory becomes
sick. These add up to previously found restrictions to impose tighter
constraints on higher-curvature gravities. The results of this paper point to
an intricate phase diagram which might accommodate similarly rich behavior in
the dual CFT side.
