Magnetized black holes surrounded by dark fluid in Lovelock-power-Yang-Mills gravity

We consider a model where static spherically symmetric black hole, in the presence of power-Yang-Mills source, is surrounded by a dark fluid with a non-linear equation of state. In this set up we construct a new class of magnetized Lovelock black hole solutions of the gravitational field equations. In particular, we work out the metric functions in both D-dimensional Einstein and Gauss-Bonnet gravities. We study thermodynamics of these black holes also and show that the mass and associated thermodynamic quantities like Hawking temperature and heat capacity depend on parameters of the dark fluid and the power-Yang-Mills magnetic source. We note that the entropy does not satisfy the area law in Gauss-Bonnet and higher order Lovelock black holes. Furthermore, phase transitions of black holes in each case are also discussed.