We study the thermodynamics and the phase structures of Reissner-Nordstr\"om and Born-Infeld black holes in AdS space by constructing ``off-shell'' free energies using thermodynamic quantities derived directly from the action. We then use these results to propose ``off-shell'' effective potentials for the respective boundary gauge theories. The saddle points of the potentials describe all the equilibrium phases of the gauge theories.
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Souvik Banerjee (2010) studied this question.
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