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 $\alpha ⋚4q^2/7$. 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 $\alpha <4q^2/7$, and for the case of $\alpha =4q^2/7$ there is no phase transition below (at) the critical point. For the last case, one finds that small and large black holes are thermodynamically distinguishable for temperatures and pressures higher than the critical ones.

通过考虑对麦克斯韦场的小幅修正，我们表明合成的黑洞解（也称为渐近 Reissner-Nordström 黑洞）经历了可重入相变并且可以具有新的相行为。我们还表明，Reissner-Nordström 黑洞的这种小的非线性校正对解的相结构有很大的影响。它导致一个新的分类中的扩展的相空间中提供的非线性参数的值的正则系综α感$\alpha ⋚4q^2/7$. 我们将研究这三类并调查与标准 Reissner-Nordström 解的偏差。有趣的是，我们发现存在重入相变$\alpha <4q^2/7$，对于 $\alpha =4q^2/7$在临界点以下没有相变。对于最后一种情况，人们发现小黑洞和大黑洞在温度和压力高于临界值的情况下在热力学上是可区分的。