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We study thermodynamics and critical behaviors of higher-dimensional Lovelockblack holes with non-maximally symmetric horizons in the canonical ensemble ofextended phase space. The effects from non-constancy of the horizon of theblack hole via appearing two chargelike parameters in thermodynamic quantitiesof third-order Lovelock black holes are investigated. We find that Ricci flatblack holes with nonconstant curvature horizon show critical behavior. This isan interesting feature that is not seen for any kind of black hole in Einsteinor Lovelock gravity in the literature. We examine how various interestingthermodynamic phenomena such as standard first-order small-large black holephase transition, a reentrant phase transition, or zeroth order phasetransition happens for Ricci flat, spherical, or hyperbolic black holes withnonconstant curvature horizon depending on the values of Lovelock coefficientand chargelike parameters. While for a spherical black hole of third orderLovelock gravity with constant curvature horizon phase transition is observedonly for $7\leq d \leq11$, for our solution criticality and phase transitionexist in every dimension. With a proper choice of the free parameters, alarge-small-large black hole phase transition occurs. This process isaccompanied by a finite jump of the Gibbs free energy referred to as azeroth-order phase transition. For the case $\kappa=-1$ a novel behavior isfound for which three critical points could exist.

Extended phase space thermodynamics for Lovelock black holes with non-maximally symmetric horizons