Multicritical Phase Transitions in Lovelock AdS Black Holes

We demonstrate that black holes in order $N\ge 4$ Lovelock gravity can exhibit multicritical phase behaviour. We show an explicit example of a quadruple point in $d=10$ fourth-order Lovelock gravity and a quintuple point in $d=14$ sixth-order Lovelock gravity. We also demonstrate that multi-criticality can be realized for uncharged, non-rotating black holes by highlighting a new type of multi-critical point between black holes and thermal radiation. We discuss the methodology used and make comparisons to other black hole multi-critical points in terms of the Gibbs phase rule.