Abstract
After considering the effect of the generalized uncertainty principle (GUP), we investigate the thermodynamic critical behaviors of the Schwarzschild-AdS (SAdS) black hole and the Reissner-Nordström-AdS (RN-AdS) black hole in four-dimensional spacetime. It is shown that for the SAdS black hole the Hawking-Page phase transition no longer always occurs under a certain condition which is replaced by a zero-order phase transition from the thermal AdS space to the large stable black hole. For the RN-AdS black hole, besides the usual small/large black-hole phase transition, an interesting reentrant phase transition also appears. This critical behavior is very similar to that of the Kerr-AdS black hole in higher-dimensional spacetime .
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