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In this work we obtain a static spherically symmetric charged black holesolution in the framework of minimal Horndeski gravity with additional Maxwelland Yang-Mills fields. The obtained solution is examined, in particular itsasymptotics are studied. Thermodynamics of the black hole is investigated,namely we use an effective surface gravity to derive black hole temperature. Toobtain the first law of black hole thermodynamics the Wald method is applied.We also use the extended thermodynamics approach, namely it allows us to derivethe Smarr relation, Gibbs free energy and the thermal equation of state. Thestudy of thermal values in the extended space shows rich phase behaviour, inparticular domain where the first order phase transition takes place and thecritical point with the second order phase transition. We also study thermalbehaviour near the critical point, obtain critical exponents and analyse theEhrenfest's equations at the critical point. Finally, we calculate thePrigogine-Defay ratio confirming the conclusion about the second order phasetransition at the critical point.

Static black hole in minimal Horndeski gravity with Maxwell and Yang-Mills fields and some aspects of its thermodynamics