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

Geometrothermodynamics of black holes in Lovelock gravity with a nonlinear electrodynamics