Critical phenomena and reentrant phase transition of asymptotically Reissner–Nordström black holes

By considering a small correction to the Maxwell field, we show that the resultant black hole solutions (also known as the asymptotically Reissner–Nordström black holes) undergo the reentrant phase transition and can have a novel phase behavior. We also show that such a small nonlinear correction of the Reissner–Nordström black holes has high effects on the phase structure of the solutions. It leads to a new classification in the canonical ensemble of extended phase space providing the values of the nonlinearity parameter α being α⋚4q2/7. We shall study these three classes and investigate deviations from those of the standard Reissner–Nordström solutions. Interestingly, we find that there is the reentrant phase transition for α