Thermodynamics and phase transitions in the Born-Infeld-anti-de Sitter black holes

We investigate the Born-Infeld-anti-de Sitter (BIAdS) black hole solutions in the four dimensions, which is a nonlinear generalization of the Reissner-Norstrom-AdS (RNAdS) black hole. We analyze all thermodynamic quantities of the BIAdS black hole in the canonical ensembles, which are characterized by the charge Q, the mass M, the nonlinear parameter b, comparing with those of the RNAdS and Schwarzschild-AdS black hole. We find the forbidden region of 0 <= bQ < 0.5 for the presence of a charged BIAdS black hole. We also discuss the Hawking-Page phase transitions in the BIAdS black holes. Here we obtain a new Hawking-Page phase transition for the bQ=0.5 critical BIAdS black hole.