Static spherically symmetric black hole in Einstein-power-Yang-Mills-dilaton theory and some aspects of its thermodynamics.

A static spherically symmetric solution is obtained and examined in the framework of Einstein-power-Yang-Mills-dilaton theory. To derive this exact solution a dilaton potential $V(\Phi)$ is taken into account. Thermodynamics of the black hole is also studied, namely we have obtained and investigated the temperature and heat capacity of the black hole which has allowed us characterize the stability of the black hole. Using the framework of the extended thermodynamic phase space we have derived the equation of state for the black hole. We have studied the Gibbs free energy of the black hole, which has the behaviour similar for other black holes with dilaton fields. To characterize the thermal behaviour of the black hole near the critical point we have written the Ehrenfest's equations and calculated Prigogine-Defay ratio.