  The objective of the present paper is to analyze the phase transition of
asymptotically anti-de Sitter (AdS) black hole solutions in Lovelock gravity in
the presence of nonlinear electrodynamics. First, we present the asymptotically
AdS black hole solutions for two classes of the Born-Infeld type of nonlinear
electrodynamics coupled with Einstein, Gauss-Bonnet and third order Lovelock
gravity, separately. Then, in order to discuss the phase transition, we
calculate both the heat capacity and the Ricci scalar of the thermodynamical
line element. We present a comparison between the singular points of the Ricci
scalar using Geometrothermodynamics method and the corresponding vanishing
points of the heat capacity in the canonical ensemble. In addition, we discuss
the effects of both Lovelock and nonlinear electrodynamics on the phase
transition points.
