Abstract
A static black hole with spherical symmetry is obtained and examined in the framework of Einstein-Yang-Mills-dilaton theory. The obtained black hole solution allowed us to derive and investigate entropy, temperature, and heat capacity. To better examine the thermodynamics of the black hole, extended phase space is also used. On this ground, the equation of state is obtained and studied. We also investigate the Gibbs free energy and it is shown that below the critical temperature the system demonstrates phase transitions of the first as well as of the zeroth order, which is a notable feature for other types of dilaton black holes. At the end, critical exponents for the black hole are calculated.
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